Question

The ratio in which the line joining $(2,-4,3)$ and $(-4,5,-6)$ is divided by the plane $3x+2y+z-4=0$ is

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

Answer 1

The correct option is C $-1:4$

A line passes through the points $(2,-4,3)$ and $(-4,5,-6)$

The equation of the line can be written as $t=\frac{x-2}{-4-2}=\frac{y+4}{5+4}=\frac{z-3}{-6-3}$

$\therefore x=-6t+2,y=9t-4,z=-9t+3$

Substituting this in equation of the plane, we get $-18t+6+18t-8-9t+3-4=0$

$\Rightarrow t=\frac{-1}{3}$ and the point becomes $(2+2,-3-4,3+3)$ i.e. $(4,-7,6)$

Let this point divide the line joining $(2,-4,3)$ and $(-4,5,-6)$ in the ratio $m:n$,

$\therefore \frac{-4m+2n}{m+n}=4$

$\therefore -4m+2n=4m+4n$

$\therefore -8m=2n$

$\therefore m:n=-1:4$