Question

Let vector a, vector b, and vector c be three non-zero vectors such that no two of these are collinear. If the vector (a + 2b) is collinear with vector c and vector (b + 3c) is collinear with vector a (λ being some non-zero scalar), then  vector (a + 2b + 6c) equals 

(A) 0 

(B) λb 

(C) λc 

(D) λ

Answer 1

Answer is (A) 0

As vector(a + 2b)  and vector c are collinear, so

From Eqs. (3) and (4), 

(λ + 6)c = (2μ + 1)a

But vector a and vector c are non-zero, non-collinear vectors, therefore