# Vector Analysis

## Homework Statement

Let x,y is in Vn, such that x is not equal to zero.
Show that you can find vectors y and y// is in Vn such that y=y + y// and y// is parallel to x and y is perpendicular to x.

x//y => x=ky
x.y=0 if x┴y

## The Attempt at a Solution

I calculated the components of y along y and y// and showed that the synthesis of these gives y. I was adviced to use x as well. So I need different method.

By supposing y//=kx,
y=y-y//
we write,
kx.(y-y//)=0
and I was asked to find k and show,y=y + y//. I have no idea how to proceed after the above line.

Thank You

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jbunniii
Homework Helper
Gold Member
Do you know how to project a vector onto another vector?

I was suggested not to use vector projections that are in trigonometric forms.
As for the y||=(x.y/x^2).x form,
I know that what I can do is find
y||=(y.kx/(kx)^2).kx [sorry, k is not bold here]
and yperp.=y-xk.,
I have no idea hence forth.

jbunniii