Question on Vectors and Components (NOT HW)

[037810]

Okay, let's say there's 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.

 

[slider142]

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 c_a and c_b such that c = c_aa + c_bb. 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.

 

[037810]

hmm... but drawing wise, they are the same?

 

[chiro]

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.