Question on Vectors and Components (NOT HW)

  • Thread starter 037810
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  • #1
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Okay, let's say theres vector a,b and c

What would be the difference between


projection of c on a and b

and

components of c along a and b


I thought they were the same...

thanks.
 

Answers and Replies

  • #2
1,013
70
The projections are like putting c and a or b tail to tail and dropping a perpendicular from the tip of c to the line defined by a or b and measuring from the tail of a or b to the intersection. In an inner product space with inner product <.,.>, the projection onto b can be calculated by <b, c>/||b||.
The components of c with respect to a and b are the numbers ca and cb such that c = caa + cbb. In the case that c is the sum of a and b, the components with respect to a and b are (1, 1). By the parallelogram law, this obviously does not correspond to the projection unless a and b are orthogonal unit vectors.
 
  • #3
20
0
hmm... but drawing wise, they are the same?
 
  • #4
chiro
Science Advisor
4,790
132
Drawing wise they should be the same as saying what the poster above said by
grabbing the vector a and the vector c (we are projecting a onto c in this case) and its just the length of a in the c direction.

With regards to your question i'm pretty sure you have the right idea.
 

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