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,
and I was asked to find k and show,y=y┴ + y//. I have no idea how to proceed after the above line.