Question

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

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

Answer 1

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

Given that xz plane divides line joining (1, -1 , 5) and ( 2 , 3 , 4) in the ration p:1

we know that,

if plane divides at some point P in m:n ration,

then $P=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n})$

As it is given, it divides in P : 1 ratio, the point would be $P=(\frac{2P+1}{P+1},\frac{3P-1}{P+1},\frac{4P+5}{P+1})$

As P lies in xz plane (given), y = 0

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

Therefore, $P+1=\frac{1}{3}+1=\frac{4}{3}$

$\therefore P+1=\frac{4}{3}$