The ratio in which the plane $\bar{r}$. $(\hat{i}-2 \hat{j}+3 \hat{k})=17$ divides the line joining the…
The ratio in which the plane $\bar{r}$. $(\hat{i}-2 \hat{j}+3 \hat{k})=17$ divides the line joining the points $-2 \hat{i}+4 \hat{j}+7 \hat{k}$ and $3 \hat{i}-5 \hat{j}+8 \hat{k}$
10:3
$3: 10$
$5: 3$
$4: 5$
Solution
Let the required ratio be $\lambda: 1$ then the point of division lies on the plane.
$\begin{aligned} & \frac{3 \lambda-2}{\lambda+1}-2 x \frac{-5 \lambda+4}{\lambda+1}+3 \times \frac{8 \lambda+7}{\lambda+1}=17 \\ & \Rightarrow \lambda=\frac{3}{10}\end{aligned}$
The required ratio is $3: 10$