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Question: Answered & Verified by Expert
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
MathematicsThree Dimensional GeometryTS EAMCETTS EAMCET 2022 (19 Jul Shift 2)
Options:
  • A $\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}$
  • B $\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}$
  • C $\frac{3}{\sqrt{46}}, \frac{-1}{\sqrt{46}}, \frac{6}{\sqrt{46}}$
  • D $\frac{1}{\sqrt{14}}, \frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$
Solution:
2692 Upvotes 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
$$
\frac{1}{\sqrt{6}}, \frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}} \text { (Given, } \mathrm{D}=(2,1,6)
$$

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