Question

Let $a$, $b$ and $c$ be three non-zero vectors such that no two of these are collinear. if the vectors $a+2b$ is collinear with $c$ and $b+3c$ is collinear with $a$.then $a+2b+6c$ is equal to :

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

Answer 1

Answer: (A)

$0$

Given that $a,b,c$ are three non zero vectors such that no two of them are collinear

Given $a+2b$ is collinear with $c$ , so we get $a+2b=xc$

Given $b+3c$ is collinear with $a$ , so we get $b+3c=ya$

By subtracting both we get $(1+y)a+b-(3+x)c=0$

Here put $y=-\frac{1}{2}$ and $x=-6$ , we get $a+2b+6c=0$

Therefore option $A$ is correct