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Old 31-01-2017, 07:04 PM   #1
untoldbattles
 
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Advanced Mathematics

With regards to vectors, length of projection of a vector onto another in particular,

How is | b . a | the length of projection of a onto b ?

I've sent an email to my tutor but he hasn't gotten back to me so I was wondering if anyone could give his two cents on this

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Old 31-01-2017, 08:34 PM   #2
untoldbattles
 
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Quote:
Originally Posted by iliketea416 View Post
I think I need a little more to answer the question but if you have two vectors, a and b, and draw straight lines through them until the meet, the angle in between is c (just an example letter). To find the scalar product of the two vectors a and b then a.b = /a//b/cos c (sorry, I don't know how to do vertical bars on this computer). Is that what you mean?
I understand that a.b = |a| |b| cosc , but my tutor mentioned that |b . a| is the length of the projection of vector b onto vector a. However, I don't see how it is so, as to my knowledge, the formula would be |b . arrow cap a|

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Old 31-01-2017, 08:38 PM   #3
untoldbattles
 
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P.s by "arrow cap a", I'm referring to the cap of vector a but I don't know how to put that inverted "v" above the letter "a"

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Old 31-01-2017, 11:45 PM   #4
untoldbattles
 
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Quote:
Originally Posted by iliketea416 View Post
Okay, so the length of the projB into a is barBcos c.

Because barA barB cos c = a.b, you can divide both sides by barA to get barBcos c which is equal to the length of the projection and therefore a.b/barA

At this point, the actual vector projection is therefore a unit vector in the correct direction times this length, meaning projB = (a/barA)(a.b/barA)

Does that help?
Ohh okay, I get it now! Thank you for the information! :)

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