Question

The ratio in which the plane $\overrightarrow{r}.(\hat{i}-2\hat{j}+3\hat{k})=17$ 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. $1:5$
• B. $1:10$
• C. $3:5$
• D. $3:10$

Answer 1

The correct option is D $3:10$

Equation of plane in cartesian form is, $x-2y+3z-17=\mathrm{0.....}\left(1\right)$
Assume this plane (1) divide the line segment joining the points $(-2,4,7)$ and $(3,-5,8)$ in $m:n$ ratio.
Therefore, $\frac{m}{n}=\frac{-2-2\left(4\right)+3\left(7\right)-17}{3-2(-5)+3\left(8\right)-17}=\frac{-3}{10}<0$
Hence plane (1) divides the given line segment externally $3:10$.