Question

Let a,b and c be three nonzero vectors, no two of which are collinear. If the vector a+2b is collinear with c, and b+3c is collinear with a, then a+2b+6c =

• A. $\lambda a$
• B. $\lambda b$
• C. $\lambda c$
• D. $0$

Answer 1

The correct option is D $0$

$a+2b=\lambda c,b+3c=\mu a$
$a+2b+6c=\lambda c+6c=(\lambda +6)c$ and $a+2b+6c=a+2\mu a=(1+2\mu )a$
$\therefore (\lambda +6)c=(1+2\mu )a\Rightarrow \lambda +6=0,1+2\mu =0\Rightarrow \lambda =-6,\mu =-\frac{1}{2}.\therefore a+2b+6c=0$