Find a unit vector perpendicular to both the vectors and
Given two vectors and
Let and
We need to find a unit vector perpendicular to and.
Recall a vector that is perpendicular to two vectors and is
Here, we have (a1, a2, a3) = (4, –1, 3) and (b1, b2, b3) = (–2, 1, –2)
Let the unit vector in the direction of be.
We know unit vector in the direction of a vector is given by .
Recall the magnitude of the vector is
Now, we find.
So, we have
Thus, the required unit vector that is perpendicular to both and is.