How to find component of w which is parallel to v?

Question

This involves dot product and is a projection problem. I was able to find the magnitude of w that is parallel to to v. Although, I can't figure out how to get the component form of it.

v = 5i + 7j

w = 5i + j

||w(parallel to v)|| = 32/sqrt(74)

Answer 1

This is the magnitude. You just need a unit vector in the direction of v and then just multiply it by the magnitude.

V (unit vector) = v / (magnitude of v) = v/SQRT(74)

V = (5i + 7j)/SQRT(47)

Parallel part of w is then: V*[32/SQRT(74)]

Parellel part of w = (160i + 224j)/74