# Multi-Variable Calculus: Cross Product Expressions

Tags: calculus 3, cross product, vectors
 PF Gold P: 641 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.A vector orthogonal to u X v and u X w A vector orthogonal to u + v and u - v A vector of length |u| in the direction of v The area of the parallelogram determined by u and w 2. Relevant equations 3. The attempt at a solution (u X v) X (u X w) (u + v) X (u - v) |u|v |u X w|
 Sci Advisor HW Helper Thanks P: 25,228 Check 3. What's the length of |u|v?
PF Gold
P: 641
 Quote by Dick Check 3. What's the length of |u|v?
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 $$\frac{\vec{u}}{|\vec{u}|}\vec{v}$$.

PF Gold
P: 346
Multi-Variable Calculus: Cross Product Expressions

 Quote by 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 $$\frac{\vec{u}}{|\vec{u}|}\vec{v}$$.
you might want to check again
 PF Gold P: 641 $\frac{\vec{v}}{|\vec{v}|}$ is a unit vector in the direction of $\vec{v}$. I need to multiply the unit vector by $|\vec{u}|$. So, $|\vec{u}|\frac{\vec{v}}{|\vec{v}|}$.
 HW Helper P: 3,307 looks good

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