In what ratio does the yz-plane divide the li | vedclass

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(A) Let the ratio in which the $yz$-plane divides the line segment joining the points $A(-2, 4, 7)$ and $B(3, -5, 8)$ be $k : 1$.The coordinates of th

Vedclass · Accepted Answer

$2 : 3$

Vedclass · Answer

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

In what ratio does the $yz$-plane divide the line segment joining the points $(-2, 4, 7)$ and $(3, -5, 8)$?

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