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Section Formula

Question

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

A

1 : 4

B

- 4 : 1

C

- 2 : 3

D

3 : 2

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Solution

Verified by Toppr

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

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