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