Find a unit vector perpendicular to the plane containing the vectors and

Given two vectors 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) = (2, 1, 1) and (b₁, b₂, b₃) = (1, 2, 1)

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.