Multi-Variable Calculus: Cross Product Expressions

Dembadon

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|

Dick

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

Dembadon

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 [tex]\frac{\vec{u}}{|\vec{u}|}\vec{v}[/tex].

wukunlin

you might want to check again

Dembadon

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

So, [itex]|\vec{u}|\frac{\vec{v}}{|\vec{v}|}[/itex].

lanedance

looks good