The ratio in which the yz-plane divides the l | vedclass

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Question

(A) The equation of the $yz$-plane is $x = 0$. Let the ratio in which the $yz$-plane divides the line segment joining $A(-3, 4, -2)$ and $B(2, 1, 3)$

Vedclass · Accepted Answer

$3: 2$

Vedclass · Answer

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

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

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