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Question

Image point of (1,3,4) in the plane 2xy+z+3=0 is

A
(3,5,2)
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B
(3,5,2)
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C
(3,5,3)
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D
None of these
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Solution

The correct option is A (3,5,2)
Let P(α,β,γ) be the image of the point Q(1,3,4), so midpoint of PQ lie on the given plane
2(α+12)(β+32)+(γ+42)+3=0
2αβ+γ+9=0 ...(i)
Also PQ is perpendicular to the normal to the plane,
α12=β31=γ41 . . . (ii)
Solving (i) and (ii), we get
α=3,β=5,γ=2.

Therefore, image is (3,5,2)

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