# What is the unit vector that is orthogonal to the plane containing  ( i - 2 j + 3 k)  and  ( - 5 i + 4 j - 5 k) ?

Jun 29, 2016

$= \frac{1}{\sqrt{35}} < 1 , 5 , 3 >$

#### Explanation:

you need to calculate the vector (cross) product of these two vectors to get the normal vector

it's not clear to me how you latex matrices on here so i will draw the computation.

so the normal vector is the determinant of the matrix as shown and we get as one possible normal vector [there an an infinite number of actual formulations of this]

$\vec{n} = < 1 , 5 , 3 >$

the unit vector is therefore

$\hat{n} = \frac{1}{\sqrt{{1}^{2} + {5}^{2} + {3}^{3}}} < 1 , 5 , 3 >$

$= \frac{1}{\sqrt{35}} < 1 , 5 , 3 >$

or

$= - \frac{1}{\sqrt{35}} < 1 , 5 , 3 >$ pointing in other direction