The coordinates of the point where the line j | vedclass

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(B) Let the point $P$ divide the line segment joining $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $k:1$.Using the section formula, the coordinates of

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$(0, \frac{13}{5}, 2)$

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(B) Let the point $P$ divide the line segment joining $A(3, 5, -7)$ and $B(-2, 1, 8)$ in the ratio $k:1$.Using the section formula, the coordinates of $P$ are $(\frac{-2k+3}{k+1}, \frac{k+5}{k+1}, \frac{8k-7}{k+1})$.Since $P$ lies on the $YOZ$ plane, its $x$-coordinate must be $0$.$\frac{-2k+3}{k+1} = 0 \implies -2k+3 = 0 \implies k = \frac{3}{2}$.Substituting $k = \frac{3}{2}$ into the $y$ and $z$ coordinates:$y = \frac{\frac{3}{2} + 5}{\frac{3}{2} + 1} = \frac{13/2}{5/2} = \frac{13}{5}$.$z = \frac{8(\frac{3}{2}) - 7}{\frac{3}{2} + 1} = \frac{12 - 7}{5/2} = \frac{5}{5/2} = 2$.Thus, the point is $(0, \frac{13}{5}, 2)$.

The coordinates of the point where the line joining the points $(3, 5, -7)$ and $(-2, 1, 8)$ is intersected by the $YOZ$ plane are

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