Find a vector of magnitude 49, which is perpendicular to both the vectors and

Given two vectors and

Let and

We need to find a vector of magnitude 49 that is perpendicular to and.

Recall a vector that is perpendicular to two vectors and is

Here, we have (a₁, a₂, a₃) = (2, 3, 6) and (b₁, b₂, b₃) = (3, –6, 2)

Recall the magnitude of the vector is

Now, we find.

Thus, the vector of magnitude 49 that is perpendicular to both and is.