A point on the XOZ-plane divides the line seg | vedclass

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Question

(A) Let point $P(x, y, z)$ divide the line segment joining the points $A(5, -3, -2)$ and $B(1, 2, -2)$ in the ratio $m:1$.Since the point $P$ lies on

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let point $P(x, y, z)$ divide the line segment joining the points $A(5, -3, -2)$ and $B(1, 2, -2)$ in the ratio $m:1$.Since the point $P$ lies on the $XOZ$-plane,its $y$-coordinate must be $0$.Using the section formula,the $y$-coordinate of $P$ is given by $\frac{m(2) + 1(-3)}{m + 1} = 0$.$\Rightarrow 2m - 3 = 0 \Rightarrow m = \frac{3}{2}$.Now,we find the $x$ and $z$ coordinates using $m = \frac{3}{2}$:$x = \frac{m(1) + 1(5)}{m + 1} = \frac{\frac{3}{2}(1) + 5}{\frac{3}{2} + 1} = \frac{\frac{3+10}{2}}{\frac{5}{2}} = \frac{13}{5}$.$z = \frac{m(-2) + 1(-2)}{m + 1} = \frac{\frac{3}{2}(-2) - 2}{\frac{3}{2} + 1} = \frac{-3 - 2}{\frac{5}{2}} = \frac{-5}{\frac{5}{2}} = -2$.Therefore,the required point is $\left(\frac{13}{5}, 0, -2\right)$.

$A$ point on the $XOZ$-plane divides the line segment joining the points $(5, -3, -2)$ and $(1, 2, -2)$ at:

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