Find all vectors of magnitude that are perpendicular to the plane of and
Given two vectors and
We need to find vectors of magnitude perpendicular to and.
Recall a vector that is perpendicular to two vectors and is
Here, we have (a1, a2, a3) = (1, 2, 1) and (b1, b2, b3) = (–1, 3, 4)
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
So, a vector of magnitude in the direction of is
Observe that is also a unit vector perpendicular to the same plane. This vector is along the direction opposite to the direction of vector.
Thus, the vectors of magnitude that are perpendicular to plane of both and are.