Question

The ratio in which the join of $A(2,1,5)$ and $B(3,4,3)$ is divided by the plane $x+2y-z=0$ is:

• A. $2:3$
• B. $8:3$
• C. $1:8$
• D. $4:3$

Answer 1

The correct option is C $1:8$

We know, a plane with equation $ax+by+cz+d=0$ divides the line joining $A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ in the ratio $-\frac{a{x}_1+b{y}_1+c{z}_1+d}{a{x}_2+b{y}_2+c{z}_2+d}$
Here, the given plane is: $x+2y-z=0$
and the points are $A(2,1,5)$ and $B(3,4,3)$
Hence the ratio is: $-\frac{2+2.1-5}{3+2.4-3}=-\frac{-1}{8}=\frac{1}{8}$