Question

The ratio in which the plane $r.(\hat{i}-2\hat{j}+2\hat{k})=17$ divides the line joining the points $-2\hat{i}+4\hat{j}+7\hat{k}$ and $3\hat{i}-5\hat{j}+8\hat{k}$ is:

• A. $3:5$
• B. $1:10$
• C. $3:10$
• D. $1:5$

Answer 1

The correct option is C $3:10$

Let the plane $r.(i-2j+3k)=17$ divide the line joining the points.

$-2i+4j+7k$ and $2i-5j+8k$ in the ratio $t:1$ at the point $P.$

$\therefore P$ is $\frac{3t-1}{t+1}i+\frac{-5t+4}{t+1}j+\frac{8t+7}{t+1}k.$

This lies on the given plane,

$\therefore \frac{3t-2}{t+1}.1+\frac{-5t+4}{t+1}\left(2\right)+\frac{8t+7}{t+1}\left(3\right)=17$

$\Rightarrow 3t-2+10t-8+24t+21=17t+17$

$\therefore 20t=17-21+10=6\Rightarrow =\frac{6}{20}=\frac{3}{10}$

$\therefore$ required ratio is $3:10$.