Find the ratio in which the line segment join | vedclass

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(B) Let the $YZ$-plane divide the line segment joining $A(4, 8, 10)$ and $B(6, 10, -8)$ at point $P$ in the ratio $k:1$.Using the section formula,the

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$2:3$ (externally)

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(B) Let the $YZ$-plane divide the line segment joining $A(4, 8, 10)$ and $B(6, 10, -8)$ at point $P$ in the ratio $k:1$.Using the section formula,the coordinates of $P$ are given by $\left(\frac{6k+4}{k+1}, \frac{10k+8}{k+1}, \frac{-8k+10}{k+1}\right)$.Since $P$ lies on the $YZ$-plane,its $x$-coordinate must be $0$.Therefore,$\frac{6k+4}{k+1} = 0$.This implies $6k + 4 = 0$,so $k = -\frac{4}{6} = -\frac{2}{3}$.The negative sign indicates that the division is external.Thus,the $YZ$-plane divides the line segment in the ratio $2:3$ externally.

Find the ratio in which the line segment joining the points $(4, 8, 10)$ and $(6, 10, -8)$ is divided by the $YZ$-plane.

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