#### Question

Write the ratio in which *YZ*-plane divides the segment joining *P* (−2, 5, 9) and *Q* (3, −2, 4).

#### Solution

\[ \text{ Let the YZ - plane divide the line segment joining points } P\left( - 2, 5, 9 \right) \text { and Q } \left( 3, - 2, 4 \right) \text{ in the ratio k: 1 } . \]

\[ \text{ Using the section formula, the coordinates of the point of intersection are given by }\]

\[\left( \frac{k\left( 3 \right) - 2}{k + 1}, \frac{k\left( - 2 \right) + 5}{k + 1}, \frac{k\left( 4 \right) + 9}{k + 1} \right)\]

\[ \text{ On the YZ - plane, the X - coordinate of any point is zero } . \]

\[ \therefore \frac{k\left( 3 \right) - 2}{k + 1} = 0\]

\[ \Rightarrow 3k - 2 = 0\]

\[ \Rightarrow k = \frac{2}{3}\]

\[ \text{ Thus, the YZ - plane divides the line segment formed by joining the given points in the ratio 2: 3 internally } . \]