12.5: Equations of Lines and Planes (2/2)

Objectives:
29. Find the distance between a point and a plane.
30. Find the distance between a point and a line.
31. Find the distance between two parallel planes.
32. Find the distance between two skew lines.

[@MJsMoonwalker4life]

These are making the complicated problems so simple. I understand it so much better with your videos. Thank you! I'm using the same text book.

[@gB-gm7vy]

My calc instructor (bless her heart) uses power points as a lecture during this covid thing. I did all the homework on web assign but I just went through the motions. I didn’t really understand what was going on. Thank you for posting this video. Seeing it in action and explanation helps so much. You’re doing calc students across the world a justice. You’re a hero…thank you.

[@someguy3104]

Far better then all of my professors. If you could post videos for an entire bachelors in physics I would be set.

[@Joe-pw7zt]

you should honestly be a professor, I'm at a "top 10 public university in the nation" but have never had a professor as thorough and understanding as yourself

[@alexandraniedden5337]

Thank you!

[@alexandraniedden5337]

@randombartard I'm a high school math teacher :)

[@yungblood4884]

@randombartard linear algebra comes before calculus 2 though, doesn't it?

[@anonymous-is5uz]

She sounds like a karen

[@jonyaleon]

@@anonymous-is5uz haha yeah

[@calebereid]

I love these lectures, way better than my professor. I still have 100% in the class and this is only going to help.

[@Peter-nr1rs]

These lectures are fantastic. Thank you for posting

[@rachaelharwood9574]

I'm pretty sure the cross product at the end is supposed to be 11i+36j+20k instead of -36j like it is here in the work. When solving the determinants, you get -j(4-40)=36j. That then makes the lower case d=-266 in the equation of the plane, and then the overall distance D=95/(sqrt(1817)) which is about 2.23
Please check me if you have any time. Thank you very much!

[@BrianLee-hg3fo]

Yep. You are correct. I got the same

[@monkmonk938]

That what I say too.

[@mruchann]

for the line of intersection of planes, it is also applicable that find two points, like putting also z=1. then we can find the v vector by subtracting the points. it gives the same result (a multiple of it)

[@sivavenkateshr]

UA-cam teachers are always the best

[@ahmedmoustafa5043]

thank you

[@JC-el5fy]

you a real one!

[@solomonobonyo9372]

This was so helpful

[@kassidy8725]

isn't b supposed to be positive 36 instead of -36? for the last problem for the distance between skew lines

[@alexandraniedden5337]

You take the opposite sign of the middle term. After setting up the cross product, you should end up with . The first and last terms keep their signs, but the middle switches. I hope this helps!

[@khoapham8184]

@@alexandraniedden5337 then isn't -(-36) = 36?

[@alexandraniedden5337]

@@khoapham8184 Yes, you are correct. My mistake!

[@ruth7234]

why isnt the vector cross product at 19:53

[@adilrhyder]

That would mean you are calculating the cross product between the position vectors of two points on either line, which are not necessarily perpendicular to both lines (since the position vectors don't lie on the lines themselves). You need to calculate the cross product between the parallel vectors of either line (which is what has been done in the video above) to get the normal to both lines. .

[@user-fc2is2xo2b]

Love from India...🤩🤩🤩🤩

[@farukkkk1]

11i+36j+20k how we get this

[@mohammeddekebo8739]

I love you too

[@makuoogbuagu6383]

Pls madam stop jumping solutions and problems but nice tutorials