Question

The ratio in which the plane $2x+y+3z-6=0$ divides the line segment joining the points $(2,-1,4)$ and $(4,3,2)$ is:

• A. $5:13$ externally
• B. $5:13$ internally
• C. $9:11$ internally
• D. $9:11$ externally

Answer 1

The correct option is D $9:11$ externally

Given:
$P:2x+y+3z-6=0$ divides the line segment joining $A(2,-1,4)$ and $B(4,3,2)$ in the ratio $AP:PB$
$\Rightarrow \frac{AP}{PB}=\frac{-(a{x}_1+b{y}_1+c{z}_1+d)}{(a{x}_2+b{y}_2+c{z}_2+d)}$
$=\frac{-\left(2\right(2)+1(-1)+3(4)-6)}{\left(2\right(4)+1(3)+3(2)-6)}$
$=\frac{-9}{11}$
As the ratio is negative division is external.