# What is the unit vector that is orthogonal to the plane containing  <0, 4, 4>  and  <1, -1, 1> ?

Jan 14, 2017

Compute the cross product of the to vectors.
Compute the magnitude of the resulting vector.
Divide the resulting vector by its magnitude.
The unit vector is: $< \frac{\sqrt{6}}{3} , \frac{\sqrt{6}}{6} , - \frac{\sqrt{6}}{6} >$

#### Explanation:

Compute the cross product:

<0,4,4>xx <1,-1,1> = | (hati,hatj,hatk), (0,4,4), (1,-1,1) | = 8hati + 4hatj - 4hatk

Compute the magnitude:

$r = \sqrt{{8}^{2} + {4}^{2} + {\left(- 4\right)}^{2}}$

$r = \sqrt{96} = 4 \sqrt{6}$

The unit vector is: $< \frac{\sqrt{6}}{3} , \frac{\sqrt{6}}{6} , - \frac{\sqrt{6}}{6} >$