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

##### 1 Answer

#### Answer:

There are two steps in finding this solution: 1. Find the cross product of the two vectors to find a vector orthogonal to the plane containing them and 2. normalise that vector so that it has unit length.

#### Explanation:

The first step in solving this problem is to find the cross product of the two vectors. The cross product by definition finds a vector orthogonal to the plane in which the two vectors being multiplied lie.

=

=

=

This is a vector orthogonal to the plane, but it is not yet a unit vector. To make it one we need to 'normalise' the vector: divide each of its components by its length. The length of a vector

In this case:

Dividing each component of