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(A) Let the ratio in which the $yz$-plane divides the line segment joining the points $A(-3, 4, -2)$ and $B(2, 1, 3)$ be $k: 1$. The coordinates of th

Vedclass · Accepted Answer

$3: 2$

Vedclass · Answer

(A) Let the ratio in which the $yz$-plane divides the line segment joining the points $A(-3, 4, -2)$ and $B(2, 1, 3)$ be $k: 1$. The coordinates of the point dividing the segment in ratio $k: 1$ are given by the section formula: $P = \left( \frac{k(2) + 1(-3)}{k+1}, \frac{k(1) + 1(4)}{k+1}, \frac{k(3) + 1(-2)}{k+1} \right)$. Since the point $P$ lies on the $yz$-plane,its $x$-coordinate must be $0$. Therefore,$\frac{2k - 3}{k+1} = 0$. $2k - 3 = 0 \implies 2k = 3 \implies k = \frac{3}{2}$. Thus,the ratio is $k: 1 = \frac{3}{2}: 1 = 3: 2$.

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

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