Find the vector whose length is 3 and which is perpendicular to the vector and

Given two vectors and

We need to find vector of magnitude 3 that is perpendicular to and.

Recall a vector that is perpendicular to two vectors and is

Here, we have (a₁, a₂, a₃) = (3, 1, –4) and (b₁, b₂, b₃) = (6, 5, –2)

Recall the magnitude of the vector is

Now, we find.

Let the unit vector in the direction of be.

We know unit vector in the direction of a vector is given by .

So, a vector of magnitude 3 in the direction of is

Thus, the vector of magnitude 3 that is perpendicular to both and is.