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A point on $X O Z$ -plane divides the join of $(5,-3,-2)$ and $(1,2,-2)$ at
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Verified Answer
The correct answer is:
$\left(\frac{13}{5}, 0,-2\right)$
Let point $P(x, y, z)$ divides the line joining the points $A$ and $B$ in the ratio $m: 1$.
Since, point $P$ is on $X O Z$ -plane $\therefore y$ coordinate $=0$ $\Rightarrow \quad \frac{2 m-3}{m+1}=0$
$\Rightarrow \quad m=\frac{3}{2}$
Now, $x=\frac{3+2 \times 5}{3+2}=\frac{13}{5}$
and $z=\frac{3 \times(-2)+2 \times(-2)}{5}=-2$
$\therefore$ Required point is $\left(\frac{13}{5}, 0,-2\right)$.
Since, point $P$ is on $X O Z$ -plane $\therefore y$ coordinate $=0$ $\Rightarrow \quad \frac{2 m-3}{m+1}=0$
$\Rightarrow \quad m=\frac{3}{2}$
Now, $x=\frac{3+2 \times 5}{3+2}=\frac{13}{5}$
and $z=\frac{3 \times(-2)+2 \times(-2)}{5}=-2$
$\therefore$ Required point is $\left(\frac{13}{5}, 0,-2\right)$.
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