Question

Let a, b and c be three non - zero vectors which are pairwise non- collinear. If a + 3b is collinear with c and b + 2c is collinear with a, then a + 3b + 6c is equal to

• A. $a+c$
• B. $a$
• C. $c$
• D. $0$

Answer 1

The correct option is D $0$

$a+3b$ is col linear with $c$.

$\therefore$ $a+3b=\lambda c............\left(i\right)$

Also, $b+2c$ is col linear with $a$.

$b+2c=\mu a............\left(ii\right)$

From Eq .(i) we get

$a+3b+6c=(\lambda +6)c....\left(iii\right)$

From Eq. (ii) we get

$a+3b+6c=(1+3\mu )a...........\left(iv\right)$

From eq. (iii) and (iv) , we get

$(\lambda +6)c=(1+3\mu )a$

Since $a$ is not col linear with $c$.

$\lambda +6=1+3\mu =0$

From eq . (iv) we get

$a+3b+6c=0$

Hence, Option $D$ is correct.