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## 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.

## Homework Equations

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