Find a vector of magnitude 6, which is perpendicular to both the vectors and

Let the vectors be and , such that

We need to find a vector perpendicular to both the vectors and .

Any vector perpendicular to both and can be given as,

Let

As we know, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

So,

A vector of magnitude 6 in the direction of is given by,

Here, .

Thus, required vector is .