Help with simple vector problem?

Question

Find component w which is parallel to v.

** w and v are vectors

v = 5i + 7j

w = 5i + j

I found the magnitude of w parallel to v = 32/sqrt(74).

Using this magnitude, I need to somehow write components for the vector w = 5i + j that is parallel to v = 5i + 7j.

As said before, the parallel vector of w onto v has a length of 32/sqrt(74).

Answer 1

Maybe this will help.

If the vector is parallel to v, then its coefficient of "i" & of "j" must be in the same ratio as v.

Any you need the length to be (as you said: I didn't check your maths)

Maybe you can just scale v to the right length?

When you worked out the length, did you effectively make a scaled v vector that was unit length?  Maybe that is useful here too?

Length of v  is sqrt(5^2 + 7^2)?

Maybe you could add your working for the length of the result, or check it again?