What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # (4 i + 4 j + 2 k) #?
There are two steps in solving this question: (1) taking the cross product of the vectors and then (2) normalizing the resultant. In this case, the final unit vector is
First step: cross product of the vectors.
Second step: normalize the resultant vector.
To normalize a vector we divide each element by the length of the vector. To find the length:
Putting it all together, the unit vector orthogonal to the given vectors can be represented as: