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

Feb 4, 2016

$C = - 2 i - 11 j - 5 k$

#### Explanation:

$A = - 3 i + j - k$
$B = 2 i + j - 3 k$
$C = A X B$
$\text{cross product A X B is normal to the plane}$
$\text{C is normal to the plane}$
$C = i \left(- 3 \cdot 1 - \left(- 1 \cdot 1\right)\right) - j \left(\left(- 3 \cdot - 3\right) - \left(- 1 \cdot 2\right)\right) + k \left(- 3 \cdot 1 - 2 \cdot 1\right)$
$C = i \left(- 3 + 1\right) - j \left(9 + 2\right) + k \left(- 3 - 2\right)$
$C = - 2 i - 11 j - 5 k$