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Let $\mathrm{A}(2,5,7)$ be the image of the point $\mathrm{B}(1,-2,3)$ with respect to a plane $\pi$. Let $C$ be the point where $A B$ meets the plane $\pi$. Let $\mathrm{D}=(2,1,6)$. Then the direction cosines of $\mathrm{CD}$ are
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Verified Answer
The correct answer is:
$\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}$
Given point $\mathrm{B}(1,-2,3)$ having image $\mathrm{A}(2,5,7)$ with respect to the plane $\pi$
hence DRs of point $\mathrm{C}$ is $\left(\frac{1}{2},-\frac{1}{2}, 1\right)$
Now DEs of CD are
$$
\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}} \text { (Given, } \mathrm{D}=(2,1,6)
$$
hence DRs of point $\mathrm{C}$ is $\left(\frac{1}{2},-\frac{1}{2}, 1\right)$
Now DEs of CD are
$$
\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}} \text { (Given, } \mathrm{D}=(2,1,6)
$$
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