The ratio in which yz-plane divides the line segment joining (-3,… - Vidyadip

MCQ

The ratio in which $yz-$plane divides the line segment joining $(-3, 4, 2), (2, 1, 3)$ is:

A
$-4 : 1$
✓
$3 : 2$
C
$-2 : 3$
D
$1: 4$

✓

Answer

Correct option: B.

$3 : 2$

Let the plane divide the line in the ratio $p : 1$
A point that divides the line joining these $2$ points in the ratio $p : 1$
given by $\Big(\frac{2\text{p}-3}{\text{p}+1},\frac{\text{p}+4}{\text{p}+1},\frac{3\text{p}+2}{\text{p}+1}\Big)$
Since, this point has to lie on the $zy-$plane.
so, $2p - 3 = 0$
$\Rightarrow\text{p}=\frac{3}{2}$

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