# Arbitrary and unit vectors

1. Sep 11, 2011

### aigerimzh

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. The attempt at a solution
I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

2. Sep 11, 2011

### mathfeel

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

3. Sep 11, 2011

### HallsofIvy

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

4. Sep 11, 2011

### aigerimzh

Yes, here also I mean (Axn)xn

5. Sep 11, 2011

### HallsofIvy

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: Sep 11, 2011
6. Sep 11, 2011

### aigerimzh

I think that (Axn)xn= aj?

7. Sep 11, 2011

### HallsofIvy

No. Try again. What is Axn first?