Question

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be there non-zero vectors such that no two of these are collinear. If the vector $\overrightarrow{a}+2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ then $\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}$ equals

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

Answer 1

Answer: (A)

$0$

Let $a+2b=4c$ ……….$\left(1\right)$

$b+3c=va$ …………$\left(2\right)$

Put vector a in $\left(2\right)$

$b+3c=v(uc-2b)$

$b(1+2v)=c(uv-3)$

Since b & c are not collinear

$1+2v=0$ $\Rightarrow v=-y_2$

$uv-3=0$ $\Rightarrow u=\frac{3}{v}=\frac{3}{-y_2}=-6$

Put values in $\left(1\right)$

$a+2b=4c$

$a+2b=-6c$

$a+2b+6c=0$.