Question

The plane $P:x+2y+3z=4$ divides line joining the points $A(1,-2,1)$ and $B(2,3,-1),$ in the ratio

• A. internally in ratio $1:4$
• B. externally in ratio $1:4$
• C. externally in ratio $4:1$
• D. internally in ratio $4:1$

Answer 1

The correct option is D internally in ratio $4:1$

Given plane :$P:x+2y+3z=4$ divides line joining the points $A(1,-2,1)$ and $B(2,3,-1)$
in the ratio $\frac{AP}{BP}=-\frac{a{x}_1+b{y}_1+c{z}_1-d}{a{x}_2+b{y}_2+c{z}_2-d}$
$=-\frac{1-4+3-4}{2+6-3-4}=\frac{4}{1}$
So, plane $P$ divides segment $AB$ internally in ratio $4:1$