Question

If the $zx$-plane divides the line segment joining $(1,-1,5)$ and $(2,3,4)$ in the ratio $p:1$, then $p+1=$

• A. $\frac{1}{3}$
• B. $1$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$

Answer 1

The correct option is D $\frac{4}{3}$

Let the points be given by $(1,-1,5)$ and $(2,3,4)$.
A point that divides the line joining these $2$ points in the ratio $p:1$ is given by $(\frac{2p+1}{p+1},\frac{3p-1}{p+1},\frac{4p+5}{p+1})$.
Since, this point has to lie on the $zx$ plane, so

$3p-1=0$
$\Rightarrow p=\frac{1}{3}$
$\Rightarrow 1+p=\frac{4}{3}$