Multi-Variable Calculus: Cross Product Expressions

[Dembadon]

I would like to check my answers...

Homework Statement

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

Homework Equations

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|

 

[Dick]

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

 

[Dembadon]

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

[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 $$\frac{\vec{u}}{|\vec{u}|}\vec{v}$$.

 

[wukunlin]

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

Hmm..

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

you might want to check again

 

[Dembadon]

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

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

 

[lanedance]

looks good