Question

The ratio in which the line segment joining the points whose position vectors are $2\hat{i}-4\hat{j}-7\hat{k}$ and $-3\hat{i}+5\hat{j}-8\hat{k}$ is divided by the plane whose equation is $\hat{r}\cdot (\hat{i}-2\hat{j}+3\hat{k})=13$ is-

• A. $13:12$ internally
• B. $12:25$ externally
• C. $13:25$ internally
• D. $37:25$ internally

Answer 1

Answer: (B)

$12:25$ externally

Equation of plane in cartesian form is, $x-2y+3z-13=0$ .....(1)$Assumethisplane\left(1\right)dividethelinesegmentjoiningthepoints$(2,-4,-7)$and$(-3,5,-8)$in$m:n$ratioTherefore,$\dfrac{m}{n} = \dfrac{2-2(-4)+3(-7)-13}{-3-2(5)+3(-8)-13}= \dfrac{-12}{25} < 0$Henc,eplane\left(1\right)dividesthegivenlinesegmentexternally$12:25$.