Unit Vectors perpendicular to 2 Vectors: Find 2 unit vectors perpendicular to

a = 2i - j + 3k and b = -4i + 2j - k.

The two given vectors define a plane. The Cross Product of the vectors is perpendicular to the plane and is proportional to one of the desired unit vectors. To make its length equal to one, we simply divide by its magnitude:

.

First find the cross product:

= i[(-1)*(-1) - 2*3] - j[2*(-1) - (-4)*3] + k[2*2 - (-4)*(-1)]

= -5i - 10j

Next, find the length:

Hence

The other unit vector is

.