Find the ratio in which the YZ-plane divides | vedclass

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(A) Let the $YZ$-plane divide the line segment joining the points $A(-2, 4, 7)$ and $B(3, -5, 8)$ in the ratio $k: 1$.By the section formula,the coord

Vedclass · Accepted Answer

$2: 3$

Vedclass · Answer

(A) Let the $YZ$-plane divide the line segment joining the points $A(-2, 4, 7)$ and $B(3, -5, 8)$ in the ratio $k: 1$.By the section formula,the coordinates of the point of intersection $P$ are given by $\left(\frac{3k - 2}{k + 1}, \frac{-5k + 4}{k + 1}, \frac{8k + 7}{k + 1}\right)$.Since the point $P$ lies on the $YZ$-plane,its $x$-coordinate must be $0$.Therefore,$\frac{3k - 2}{k + 1} = 0$.This implies $3k - 2 = 0$,so $k = \frac{2}{3}$.Thus,the ratio is $k: 1 = \frac{2}{3}: 1$,which is $2: 3$.

Find the ratio in which the $YZ$-plane divides the line segment formed by joining the points $(-2, 4, 7)$ and $(3, -5, 8)$.

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