Two vectors u and v are given. u = 5j + 3k, v = −i + 2k

Question

Two vectors u and v are given.

u = 5j + 3k, v = −i + 2k

(a) Find a vector orthogonal (perpendicular) to both u and v.

(b) Find a unit vector orthogonal (perpendicular) to both u and v.

Answer 1

(a) Vector a perpendicular to u and v: a = u×v = det[(i j k) (0 5 3) (- 1 0 2)] = 10i - 3j + 5k

(b) unit vector b = a/IIaII = (10i - 3j + 5k)/√(100 + 9 + 25) = (10/√√134)i - (3/√134)j (5/√134)k