# Arbitrary and unit vectors

## Homework Statement

Let A be an arbitrary vector and let n be a unit vector in some fixed direction. Show that A=(A.n).n+(A*n)*n

## The Attempt at a Solution

I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

## Homework Statement

Let A be an arbitrary vector and let n be a unit vector in some fixed direction. Show that A=(A.n).n+(A*n)*n

## The Attempt at a Solution

I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

Most straightforward way is to write out the Cartesian components and verify. Just keep in mind that $n_x^2 + n_y^2 + n_z^2 = 1$.

HallsofIvy
Homework Helper
Again, you have used "*". What is that? The cross product? The usual notation is just "AX B".

Yes, here also I mean (Axn)xn

HallsofIvy
Homework Helper
You can set up you own coordinate system and so, without loss of generality, take n to be $\vec{i}$. Write A as $a\vec{i}+ b\vec{j}+ c\vec{c}$.

Then $A\cdot n= a$ so that $(A\cdot n)= a\vec{i}$. What are $A\times n$ and $(A\times n)\times n$?

Last edited by a moderator:
I think that (Axn)xn= aj?

HallsofIvy