Question

Let A = 2i + k, B = i + j + k and C = 4i – 3j + 7k. Find a vector R satisfying R × B = R × C and R.A = 1. 

Answer 1

Given, R × B = R × C

R × (B – C) = 0

∴ R is parallel to (B – C)

R = λ(B – C)

R = λ(– 3i + 4j – 6k) ...(i)

Also, R.A = 1

–6λ – 6λ = 1 

λ = –1/12

Thus, R = – (1/2)(–3i + 4j – 6k).