Question

The ratio in which $\hat{i}+2\hat{j}+3\hat{k}$ divides the join of $-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ is

• A. $-3:2$
• B. $1:2$
• C. $2:3$
• D. $-4:3$

Answer 1

The correct option is B $1:2$

Let $\hat{i}+2\hat{j}+3\hat{k}$ divided the join of

$-2\hat{i}+3\hat{j}+5\hat{k}$ and $7\hat{i}-\hat{k}$ in $\lambda :1$

$\left(\frac{7\lambda -2}{\lambda H},\frac{3}{\lambda H},\frac{-\lambda +5}{\lambda H}\right)=\left(1,2,3\right)$

$7\lambda -2=\lambda H$

$\begin{array}{c}6\lambda =3\\ \lambda =\frac{1}{2}\end{array}$

Then,

Option $B$ is correct answer.