# What is the unit vector that is orthogonal to the plane containing  (-2i- 3j + 2k)  and  (3i – 4j + 4k) ?

Jan 20, 2016

Take the cross product of the 2 vectors
${v}_{1} = \left(- 2 , - 3 , 2\right) \mathmr{and} {v}_{2} = \left(3 , - 4 , 4\right)$
Compute ${v}_{3} = {v}_{1} \times {v}_{2}$
$\frac{1}{\sqrt{501}} \left(- 4 , 14 , 17\right)$

#### Explanation:

The ${v}_{3} = \left(- 4 , 14 , 17\right)$
The magnitude of this new vector is:
$| {v}_{3} | = {4}^{2} + {14}^{2} + {17}^{2}$
Now to find the unit vector normalize our new vector
u_3 = v_3/ (sqrt( 4^2 + 14^2 + 17^2)); = 1/sqrt(501) (-4, 14, 17)