# Multi-Variable Calculus: Cross Product Expressions

1. ### Dembadon

662
I would like to check my answers...

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

Given nonzero vectors u, v, and w, use dot product and cross product notation to describe the following.
1. A vector orthogonal to u X v and u X w
2. A vector orthogonal to u + v and u - v
3. A vector of length |u| in the direction of v
4. The area of the parallelogram determined by u and w

2. Relevant equations

3. The attempt at a solution

1. (u X v) X (u X w)
2. (u + v) X (u - v)
3. |u|v
4. |u X w|

2. ### Dick

25,853
Check 3. What's the length of |u|v?

3. ### Dembadon

662
[STRIKE]If |u| = k, where k is some constant, then the length of |u|v would be kv1 + kv2.[/STRIKE]

Hmm..

I think I see my mistake. It should be $$\frac{\vec{u}}{|\vec{u}|}\vec{v}$$.

Last edited: Sep 8, 2011
4. ### wukunlin

388
you might want to check again

5. ### Dembadon

662
$\frac{\vec{v}}{|\vec{v}|}$ is a unit vector in the direction of $\vec{v}$. I need to multiply the unit vector by $|\vec{u}|$.

So, $|\vec{u}|\frac{\vec{v}}{|\vec{v}|}$.

6. ### lanedance

3,307
looks good

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