Finding Unit Vector that is Perpendicular

Question

If vector b=[3,6,2] and vector c=[0,0,8], find a unit vector perpendicular to both vector b and c.

Answer 1

To find a vector perpendicular to both vectors, we take the cross product of those vectors.

Let vector a = ⌈ i j k ⌉ = (6*8-0*2) i - (3*8-0*2) j + (3*0-6*0) k = 48 i -24 j + 0 k.

Ι 3 6 2 Ι

⌊ 0 0 8 ⌋

This vector has the proper orientation but is not a unit vector. To get a unit vector, we must divide this vector by its length.

u = [48, -24, 0] / √(48² + 24²) = [48, -24, 0] / √2880 = [2/√5, -1/√5, 0]