Vector Equation of a Line

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  • Опубліковано 31 січ 2025

КОМЕНТАРІ • 218

  • @asemnafiz
    @asemnafiz 10 років тому +14

    Patrick helped me in my calculus 1 and 2. Then didn't take maths for a semester and now taking linear algebra and once again Patrick's videos are helping me out. He's simply the best!

    • @KoolGNasBlackThought
      @KoolGNasBlackThought 10 років тому +1

      he helped me with calc 1 & 2 but I can't find anything useful for calc 3 :(

    • @asemnafiz
      @asemnafiz 10 років тому +1

      KoolGNasBlackThought
      Really? Actually it also depends on which book Patrick is following. For my calc 1 and calc 2 I noticed that Patrick followed the same order of chapters and same example problems as my textbook. So I could just play his playlist and revise the entire course. But, for the linear algebra I have to look here and there.I would suggest that you make your own playlist and add videos according to your course outline.

  • @tobypark2045
    @tobypark2045 11 років тому +5

    No man is single-handedly carrying me through college math right now more than this man here. Bless you Patrick!

  • @m4donner
    @m4donner 6 років тому +23

    PatrickJMT Bro, i have been watching you since I started algebra 1 in Highschool all the way past calculus 1,2, and 3 and even differential equations. You have basically helped me with my entire math career and thanks to your help I will be graduating with a degree in Nuclear Engineering with a complete understanding of differentials, integrals, the 3-D world, etc. Thank you so much Patrick!

    • @yomomomama3964
      @yomomomama3964 6 років тому +1

      make a 6000 dollar donation to this legend

    • @nicolassaba3855
      @nicolassaba3855 5 років тому +2

      congrats. Too bad you wont use any of the stuff you learned in school in the real world

  • @alcatrazclad
    @alcatrazclad 9 років тому +21

    I'm surprised that every college student ever is not subscribed to you.

  • @Mattherat203
    @Mattherat203 11 років тому +107

    At the bottom of my linear final, I will mention your name at the bottom of my paper making sure you get credit for helping me pass my semester and get a good grade :p

    • @yomomomama3964
      @yomomomama3964 6 років тому +13

      Your professor gonna be jealous and may give u a bad grade for substituting Partick for him/her, these professor's egos are krazy!

  • @DxROC
    @DxROC 11 років тому +2

    Awesome video! Had my first day of Calc 3 today and I was already lost when the teacher tried to explain this. You are the MAN Patrick!

  • @mytwohands
    @mytwohands 13 років тому +5

    Your comparison to y = b + x(m) made so much sense to me! Thanks a lot.

  • @alperensirin7497
    @alperensirin7497 11 років тому +1

    To be honest you are the best tutor and a teacher I have seen in 17 years of life. I am preparing for the olympiads and these videos are helping me alot. Thank you very very much.

  • @juanmedina1994
    @juanmedina1994 10 років тому +50

    In problem (a) was the answer suppose to be 1+2t instead of 1-2t? I'm not sure where the negative came from. Also how did we change the point (1,0,-3) into a vector?

    • @queenstrategy904
      @queenstrategy904 4 роки тому +4

      You actual do point P minus the origin aka (1,0,-3) - (0,0,0) to get a vector. He skipped that step, so I can see why it would be confusing. I agree with you on the first part

    • @frondinahishidivali5352
      @frondinahishidivali5352 3 роки тому +1

      I feel like, say (1,0,-3) be your ( Po) and your unit vector(I,j,k) be your normal vector. so you make (unit vector - Po (position vector in this case).

    • @MercedesJSchmidt
      @MercedesJSchmidt 4 місяці тому

      @@queenstrategy904 incorrect. He only subtracted the x component, not y and z. It was clearly an error.

  • @patrickjmt
    @patrickjmt  15 років тому +2

    glad you like it! : )

  • @getskillsordietrying
    @getskillsordietrying 12 років тому

    man i swear i've been youtubeing math questions for years and it always ends up being you that has the best and simple explanation. Seriously thanks a lot man. From ur fellow canadians up here :D

  • @yummayyam
    @yummayyam 12 років тому

    you are seriously the best tutor i could have ever asked for.
    without you, i wouldn't have been able to survive 3 years of math.
    only my 4th year.

  • @verahavlicek
    @verahavlicek 10 років тому +60

    In part (a), x=1+2t

    • @johnscorpion815
      @johnscorpion815 5 років тому +1

      To be sincere...am not understanding

    • @robhousehold
      @robhousehold 5 років тому +7

      correct i noticed it too

    • @marcoflores8004
      @marcoflores8004 11 місяців тому

      He accidentally changed the 2t to negative 2t when he distributed the t to given vector ​@@johnscorpion815

  • @xtraMOBx
    @xtraMOBx 12 років тому +1

    I love to use your videos the night before test to review. I always pick up on something new and it always helps me in the long run. Thank you very much for all your work.

  • @rducky01
    @rducky01 15 років тому +1

    Thank you so much for adding the multi variable videos. I can remember all thru calc 2 and Diff EQ (The past two semesters...) worrying about what I was going to do for multivariable calc 3. In fact, Thank you for all of your videos. They have been a welcome aid to my studies, and have helped me earn a B+ in calc 2. ( I work a 50 hour work week side from attending night school.)

  • @vadim8016
    @vadim8016 11 років тому +1

    I was looking at my book for good amount of time and couldnt figure it out, this video helped so much! Thanks man.

  • @allenmoody7527
    @allenmoody7527 6 років тому +1

    These videos always happen to clearly explain what I've been trying to understand for hours

  • @sarahmitchell8344
    @sarahmitchell8344 3 роки тому +1

    This made so much sense! Thank you! (also your little comparison to y=mx+b was super helpful)

  • @MrAlbashiri
    @MrAlbashiri 9 років тому

    I don't know what would i do without ur videos. huge love to u

  • @patrickjmt
    @patrickjmt  14 років тому

    @magicalchair no, you are correct; i do make a mention of this using annotations so i guess that is why no one else has bothered to point it out (cause i do!)

  • @WicKedM3
    @WicKedM3 11 років тому +21

    Fantastic... You did exactly the same problem I had trouble with from my hw... What are the odds?

  • @DarkTiesandRibbons
    @DarkTiesandRibbons 13 років тому

    This is amazingly simple, yet somehow my math book managed to make it seem as if the goal was to divide by zero. You've made my life infinitely easier, thank you.

  • @batzuljohnthomas6094
    @batzuljohnthomas6094 2 роки тому

    Even 12 years later this video still works (at least for me), tysm dude

  • @patrickjmt
    @patrickjmt  13 років тому

    @MrFrozenRanger glad you liked it : )

  • @hollyvuong1464
    @hollyvuong1464 10 років тому

    First day learning this, didn't get it, watched this video then...BWWOOOSSHH!!! Mind blown! Helped a lot! Thank you, Patrick!

  • @mochigojo9753
    @mochigojo9753 6 років тому

    you dont know how popular you are in our university well specially among students you saved many lives and calc grades i hope u know that

  • @Fg5x3
    @Fg5x3 13 років тому

    Didn't understand the last two weeks of class. Final's coming up; time to cram-study with your videos. Thanks for saving my grade :)

  • @Arzenimus
    @Arzenimus 14 років тому

    Cool, this actually starts smelling like fun.. And no matter I'm gonna fail the exam in few days (due to my usual laziness -.-), you are a great teacher!

    • @Arzenimus
      @Arzenimus 3 роки тому

      no idea it was 10 years ago lol

  • @sunnyblonde93
    @sunnyblonde93 14 років тому

    thank you! i missed a few days of class due to AP testing and i had no idea how to do this. thanks again :)

  • @EffectTheDoppler
    @EffectTheDoppler 13 років тому

    I THINK YOU ARE GONNA SAVE MY LIFE ON MIDTERM TOMORROW, 5 HOURS PAST AND I THINK I GOT THE CALCULUS 2
    !!!! GO PATRICK GO !!!!

  • @troyholfeld7033
    @troyholfeld7033 12 років тому

    I owe you a beer or 12.. you helped me through this class like no other. See ya next semester!

  • @xabcx
    @xabcx 15 років тому

    patrick, you are absolutely incredible. they should sell portable versions of your help videos.

  • @JFrameMan
    @JFrameMan 12 років тому

    wow could not believe it's that simple. What a great way to explain it all.

  • @JanaJana-yw3sg
    @JanaJana-yw3sg Рік тому

    the position vectors of the points A and B are (1.4.6.) and (3.5.7) .find the vector equation of the line AB and find the points where the line intersects the coordinate planes

  • @forrest3810
    @forrest3810 9 років тому +14

    Very helpful as always. I owe you my tuition!

    • @patrickjmt
      @patrickjmt  9 років тому +9

      +Forrest Unterbrink send it on over or become a patron on the website 'Patreon!' :)

    • @sheharyarahmad7078
      @sheharyarahmad7078 8 років тому

      +patrickJMT heheheheheh

    • @karjeezy723
      @karjeezy723 7 років тому

      shut your money hungry ass up.

  • @MN400368
    @MN400368 11 років тому

    Thank you for showing visual and algebraic representations. You are amazing!

  • @ilovemusic24ful
    @ilovemusic24ful 11 років тому

    This is great. But I'm working on a problem where the solution states the "direction numbers" that are used in the composition of the parametric equations, are just the numerators of the resulting vector between the two points, which of course, are fractions. Points in problem: (5,-3,2) and (-2/3,2/3,1).

    • @ilovemusic24ful
      @ilovemusic24ful 11 років тому

      ^ ...I forgot to say this...I don't know why the numerators are the only numbers used in creating the parametric equations. Vector I got was, -17/3,11/3,-1

  • @cookiemuenster
    @cookiemuenster 12 років тому

    You're an amazing teacher! Please just come to our high school and teach us!

  • @firasfreja4560
    @firasfreja4560 12 років тому +2

    nice explanation, but in the first question, should the answer for x be 1+2t instead of 1-2t :) ?

  • @xefroster
    @xefroster 15 років тому +1

    awesome videos all of them. im from melbourne aus. studying in melbourne uni. honestly you got me through calc1 and calc2 with hd (80%) god bless you :)

    • @wolfgang5496
      @wolfgang5496 3 роки тому

      omg, what are you currently doing right now that you've graduated?

  • @patrickjmt
    @patrickjmt  13 років тому

    @theOman333 not sure. so many examples, i do not remember them all

  • @patrickjmt
    @patrickjmt  13 років тому

    @thezsk1 then find a pay site and pay for it. then you will not have to deal with the ads.

  • @MrBeamer2011
    @MrBeamer2011 10 років тому +79

    So part (a) is not correct.... It shouldn't be negative 2t it should be positive

    • @sulaimanmosavel1004
      @sulaimanmosavel1004 10 років тому +2

      *****
      Coz of my sucky internet I normally download first then watch but thank you the confirmation was a bit worried about that (-) sign

    • @patrickjmt
      @patrickjmt  10 років тому +16

      ***** thanks Terrify for pointing this out!

    • @lock0nstratos416
      @lock0nstratos416 10 років тому +3

      Okay awesome I'm not the only one to realize this. Is their a way to see annotations from a smart phone?

  • @brilliantfranz
    @brilliantfranz 15 років тому

    niceeeeeee
    please more and thanks for the ones you've already uploaded

  • @147Ptm
    @147Ptm 5 років тому

    I fucking love you dude, you literally saved my semester

  • @icemerlin92
    @icemerlin92 11 років тому

    It seems to be a different parametric equation, but it's actually the same. For the one Patrick provided, if you sub t=1, you'd get (-4,3,0). For the one janmola provided, if you sub t=-1, you'd get (1,3,2). Therefore, the paramter t is just a variable that allows you to get all the points of on the vector equation with different values of t. Hope I answered your question. :)

  • @MrFrozenRanger
    @MrFrozenRanger 13 років тому

    Hey Patrick, great work, completely clear, very nice!!!!

  • @yakarotsennin3115
    @yakarotsennin3115 7 років тому

    Once again clearing up any confusion. Thanks!!

  • @No0bZai96
    @No0bZai96 9 років тому

    Oh god i am so glad there is someone contributed such great video
    Thank you sir u are awesome :DD

  • @scrabjong
    @scrabjong 9 років тому +1

    Can you give an example of perpendicular vectors? For example, write an equation for the points (0,0,0), (a,b,c) and (m,n,p) that form a right triangle with the right angle at the origin.

  • @mikaelayuki7910
    @mikaelayuki7910 6 років тому

    the analogy is a legend!

  • @SocomBandit
    @SocomBandit 15 років тому

    i was wondering if u could do a video for the vector equations that includes the Cartesian form and what its all about?

  • @mrjonathanvella
    @mrjonathanvella 10 років тому +1

    In the second problem you said that the direction of the vector does not matter in this case. Does that mean that i could have subtracted the second equation from the first? Thanks.

  • @Magicboyz156
    @Magicboyz156 11 років тому

    oh man thanks so much! for this vector stuff. It's a life saver! good job man.

  • @rboy879
    @rboy879 11 років тому

    U should be a professor period.

  • @theOman333
    @theOman333 13 років тому

    That was a really good video, do u have a video where you explain the vector equation of a line wherere u need to find the perpindicular vector?

  • @fisslewine1222
    @fisslewine1222 8 років тому +1

    Is this basically the same approach to fining a line that passes through a point with a direction vector?

  • @habibullah17
    @habibullah17 14 років тому

    thanks for the help, made it easy to understand

  • @andrewku6683
    @andrewku6683 5 років тому

    so we assume that the vector parallel to the line going through both points is *on* the line going through both points? how can they be parallel if they're touching?

  • @kaciewassef2387
    @kaciewassef2387 Рік тому

    THANK YOU SO MUCH!! this was so helpful

  • @Zezing1
    @Zezing1 13 років тому

    Thankyou wow I spent so long trying to figure this out until i watched this!

  • @hydrogen1562
    @hydrogen1562 6 років тому

    5:33 if you chose to use the other vector (-4,3,0) instead of (1,3,2) in the equation, what would change? How do you know which one to use as the a in r=a+tb?

  • @kateelliott7158
    @kateelliott7158 5 років тому +1

    How do you calculate if line is orthogonal to eqn?

  • @ILovePeanutButer7181
    @ILovePeanutButer7181 13 років тому

    @Ratman2050 no, you're adding the -5, not subtracting it

  • @Ramokone89
    @Ramokone89 12 років тому

    When you distribute t, why does 2change to -2t instead of 2t?

  • @JKingLXI
    @JKingLXI 13 років тому

    hi patrick, third semester of cal with an B+ and an A- thx to u! funny i did better in calc 2 than in calc 1. could you please talk about symmetric equations of vector line?
    thank you

  • @vugina123
    @vugina123 12 років тому

    DUDE YOU'RE AWESOMEEEEEEEEE!

  • @Mrster
    @Mrster 15 років тому

    Good. Seems to be easier this way. But what happens if you have a line that goes through 2 points AND is parallel to say 3 vectors?

  • @patrickjmt
    @patrickjmt  15 років тому

    lol, are you serious?
    sure, anything else you need?
    i just sit and stare at my computer all day ....

  • @hshibeeb
    @hshibeeb 8 років тому

    Well explained, thanks man

  • @cameronismadd69
    @cameronismadd69 12 років тому

    when he multiplies through by 't' why does the 2 for the x coordinate become -2?

  • @hohodsj
    @hohodsj 11 років тому

    I have exactly the same question as you. Plz tell me when you figured out.

  • @Airsz
    @Airsz 11 років тому

    I have a question from my textbook. It is asking for a vector equation and the parametric equations for each scalar equation given.
    Eg. x+2y=6. -Ans.[2,2]+t[2,1] and x=2-2t/y=2+t.

  • @frondinahishidivali5352
    @frondinahishidivali5352 3 роки тому

    Thank you very much, I had the same problem and now I understand 💯%. Woow, this is really amazing!!!

  • @Dleger13
    @Dleger13 12 років тому

    how would you do this if v was given in the form of its symmetric equations?

  • @janmola
    @janmola 11 років тому

    So it doesn't matter which point you choose to be r(0) ? If you chose (-4,3,0) to be r(0) wouldn't that result in a different parametric equation -( -4-5t,3,-2t)

  • @carolinebouvie7084
    @carolinebouvie7084 11 років тому

    How do you express a vector in terms of another vector?
    Like vector A is a function of vector r: A(r) ?

  • @madae1670
    @madae1670 10 років тому

    For question 1, how would you find the cartesian equation?

  • @picosdrivethru
    @picosdrivethru 5 років тому

    nice! m is basically the vector in the vector form

  • @SPEEDYLEARN
    @SPEEDYLEARN 3 роки тому

    how negative is come with 2 ? at 4:14
    you said that negative 2t

  • @journeyboy-.9971
    @journeyboy-.9971 8 років тому

    Very Helpful. Tnx a lot Patric

  • @leonidalekseyev3809
    @leonidalekseyev3809 9 років тому

    Helpful tips, thanks!

  • @CptNeutralize
    @CptNeutralize 13 років тому

    clear & precise

  • @RiteofWriters
    @RiteofWriters 12 років тому

    How do you write an equation for a line that's perpendicular to a point?

  • @tarmizinazarudin1110
    @tarmizinazarudin1110 11 років тому

    Patrick, why did you leave the answer as it is, instead of (-4t,3t,0t) ? is that how it is suppose to be?

  • @cngzz1zyvov
    @cngzz1zyvov 8 років тому

    thanks! I like the "analogy" of using y=b+xm

  • @jakeaudi297
    @jakeaudi297 11 років тому

    At 4:18 when u destrubited the t it supposed to be positive 2t. Not negative

  • @Hereson
    @Hereson 11 років тому

    Thank you!

  • @dazz95273
    @dazz95273 14 років тому

    ...ur a freak bro...a lifesaver...a godsend

  • @Tinadecember
    @Tinadecember 10 років тому

    this was so helpful thank you!

  • @dashz92
    @dashz92 11 років тому

    a very nice tutorial my frd, thank you

  • @lmfao88xm
    @lmfao88xm 9 років тому

    This was brilliant.

  • @DMSAProductions
    @DMSAProductions 10 років тому

    Amazing!!! Thank you very much! You helped me A LOT!!!!!

  • @patrickjmt
    @patrickjmt  15 років тому

    i also give foot rubs and mow lawns upon request

  • @magicalchair
    @magicalchair 14 років тому

    in the first example, shouldn't it be a positive 2t? why is it negative? i feel like someone would have pointed this out already, so I must be wrong.

  • @dtballer42911
    @dtballer42911 12 років тому

    why did you change the 2 to -2t instead of 2t in the first problem

  • @davidt0504
    @davidt0504 14 років тому

    how do I spend the last few days before calculus final? watching PatrickJMT videos haha

  • @wolfdefender01
    @wolfdefender01 11 років тому +1

    you're a life saver!

  • @robodoctor
    @robodoctor 14 років тому

    how did you get that parallel vector's coordinates?

  • @patrickjmt
    @patrickjmt  14 років тому

    @ARQ911 ringo starr