Hi could please tell me the difference between the formula which uses c2 = a2+b2 + 2ab cos theta and c2 = a2+b2 -2ab cos theta when finding the resultant force? Thanks
@@MrHelpfulNotHurtful @Nick DiFilippo , I have been accustomed to using the same formula with yours, but I have come across the other formula in a book and in some video presentation and websites that make me wonder whether it is a separate formula to use in a special case or a typo error. However, judging from the textbook presentation, it seemed a derivation of formula. : R2 = a2+b2 + 2ab cos (180 - theta) Leading to: R2 = a2+b2 - 2ab cos theta. Not, sure if the first formula is tobe used it if the angle given in the problem is to be subtracted to 180, and use the second formula, if subtraction of angles will not be done.
@@michaelgalario6655 I see. Well, I’ve never heard of it and there is probably no need for it. I think we can solve all of the problems with the more common formula.
@@MrHelpfulNotHurtful , I have browsed the net and saw some examples using it. Do you have an email? I'll be happy to share with you the page of the book where I saw it. I have seen some people.using it and this made me really confuse too that I started reading about it, but my reading doesn't lead to anyt credible references and so I resorted to watching videos and stumbled yours. This is making me really curious whether some people using the +2ab cos theta might have inadvertently learned the wrong thing or there really exist such a thing. This is making my head itch. 😅
Does this video work with this question? " vector a= 15m; 60° south of west, vector b= 10m;going north, and vector c=12m; 30° North of east find the resultant and direction"
Cindy Chan You are right. This lesson assumes that you already know the law of cosines. Usually the vector unit is taught after the law of cosines. Here is lesson on the law of cosines. ua-cam.com/video/qq6kRMCCb64/v-deo.html
It depends on the information you are given. The Law of Cosines can solve the triangle if you are given SAS or SSS. The Law of Sines will work if you are given AAS, ASA or SSA. In the first example in the video we had SAS (side-angle-side) so I knew to use the Law of Cosines.
For example #2; X = 105, but looking at the drawing the angle looks less than 90. So would X actually equal 180-105 = 75? Thanks for the awesome video! It is extremely helpful
No. The answer is correct, it’s just that the original picture is not drawn to scale. You know how the hypotenuse is always the biggest side? If you look at the green resultant of 28, it is in a similar position as a hypotenuse. It should be the longest side if the original drawing was realistic. However, one of the component forces was 32 which is bigger than 28. If the original drawing had been to scale, the angle between the vectors would have looked like 105 degrees. Sometimes they purposely avoid drawing the diagram to scale so you cannot try to guess the answer from the picture.
In this video I showed two methods. The second method works for three vectors at once. Convert all three vectors to component form and combine all three into single component form resultant. You can then find the magnitude and direction as shown.
What’s the time stamp? I looked at example 2 and the answer was 105 degrees. In order to help you I need to know what you did differently than I did. Did you type the exact same expression in your calculator? Is your calculator in degree mode?
Dude thank you I understood your teaching more than my Physics teacher
Yay!! I got your back. 😎
If a question says that angle between vector A and B is 30. What is this angle? Is it when vectors are aligned tail to tail or head to head?
This is the kind of video am looking since
I’m so glad I could help. 😊
Hi could please tell me the difference between the formula which uses c2 = a2+b2 + 2ab cos theta and c2 = a2+b2 -2ab cos theta when finding the resultant force? Thanks
The first one is not a thing. It’s is only -2ab cos C.
@@MrHelpfulNotHurtful @Nick DiFilippo , I have been accustomed to using the same formula with yours, but I have come across the other formula in a book and in some video presentation and websites that make me wonder whether it is a separate formula to use in a special case or a typo error. However, judging from the textbook presentation, it seemed a derivation of formula. :
R2 = a2+b2 + 2ab cos (180 - theta)
Leading to:
R2 = a2+b2 - 2ab cos theta.
Not, sure if the first formula is tobe used it if the angle given in the problem is to be subtracted to 180, and use the second formula, if subtraction of angles will not be done.
@@michaelgalario6655 I see. Well, I’ve never heard of it and there is probably no need for it. I think we can solve all of the problems with the more common formula.
@@MrHelpfulNotHurtful , I have browsed the net and saw some examples using it. Do you have an email? I'll be happy to share with you the page of the book where I saw it. I have seen some people.using it and this made me really confuse too that I started reading about it, but my reading doesn't lead to anyt credible references and so I resorted to watching videos and stumbled yours. This is making me really curious whether some people using the +2ab cos theta might have inadvertently learned the wrong thing or there really exist such a thing.
This is making my head itch. 😅
@@michaelgalario6655 😄 burtond1 @me.com
Does this video work with this question? " vector a= 15m; 60° south of west, vector b= 10m;going north, and vector c=12m; 30° North of east find the resultant and direction"
Cindy Chan You are right. This lesson assumes that you already know the law of cosines. Usually the vector unit is taught after the law of cosines. Here is lesson on the law of cosines.
ua-cam.com/video/qq6kRMCCb64/v-deo.html
Cindy Chan Yes. The second method will work great for this problem. Turn all three into component form and then combine like terms.
Here is another video with more examples of solving vector word problems using component form: ua-cam.com/video/DYD6m_4BWl4/v-deo.html
Here is a link to my whole vector playlist. The word problems start at Day 16: ua-cam.com/play/PLUq8yM4tK_aUVqdC9PJx8TsUPi0pcWZ5r.html
@@MrHelpfulNotHurtful OMG thank you so much!!! I literally can't understand anything from my teacher.
what drawing software are you using?
I am writing with a Wacom Intuos tablet pen on a OneNote document while recording with screencast-o-matic.
@@MrHelpfulNotHurtful Thank you so much for the reply this will truly help me and my students.
why do you use cos? How do you know when to use sin instead?
It depends on the information you are given. The Law of Cosines can solve the triangle if you are given SAS or SSS. The Law of Sines will work if you are given AAS, ASA or SSA. In the first example in the video we had SAS (side-angle-side) so I knew to use the Law of Cosines.
Thank you very much!
You are very welcome. 😊
20:50
For example #2; X = 105, but looking at the drawing the angle looks less than 90. So would X actually equal 180-105 = 75?
Thanks for the awesome video! It is extremely helpful
No. The answer is correct, it’s just that the original picture is not drawn to scale. You know how the hypotenuse is always the biggest side? If you look at the green resultant of 28, it is in a similar position as a hypotenuse. It should be the longest side if the original drawing was realistic. However, one of the component forces was 32 which is bigger than 28. If the original drawing had been to scale, the angle between the vectors would have looked like 105 degrees. Sometimes they purposely avoid drawing the diagram to scale so you cannot try to guess the answer from the picture.
What if there's three?
In this video I showed two methods. The second method works for three vectors at once. Convert all three vectors to component form and combine all three into single component form resultant. You can then find the magnitude and direction as shown.
Thankyou sir
You are very welcome. 😊
In example 2 I got 75° not 101
What’s the time stamp? I looked at example 2 and the answer was 105 degrees. In order to help you I need to know what you did differently than I did. Did you type the exact same expression in your calculator? Is your calculator in degree mode?
@@MrHelpfulNotHurtful sorry I think I have gotten it. Thanks
See that of example 3 I got 25.4
Did you type the exact same expression into your calculator or did you get a different expression?
@@MrHelpfulNotHurtful yes I type the same example in my cal and get different answer