Perpindicular vectors questions

**HFLER** · March 10th 2009, 04:29 PM

Hi all,

I have (what I think is) a relatively simply calculus question: I am trying to find the unit vector u when I know that it is perpendicular to both v=i-2j+3k and w=2i+j-k.

If anyone has any insight, I'd greatly appreciate it. Thanks!

**o_O** · March 10th 2009, 05:12 PM

Let $\vec{c}$ be the vector that results from taking the cross product of both $\vec{v}$ and $\vec{w}$ .

Recall that $\vec{c} \perp \vec{v}$ and $\vec{c} \perp \vec{w}$ .

All that remains is to simply use the formula: $\hat{c} = \frac{\vec{c}}{||\ \vec{c} \ ||}$

**Plato** · March 10th 2009, 05:45 PM

$u = \frac{{v \times w}}<br /> {{\left\| {v \times w} \right\|}}$

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