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Question

The image of point P(1,2,3) in the plane 2x+3y4z+22=0 measured parallel to the line x1=y4=z5 is

A
(2,2,8)
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B
(3,6,13)
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C
(2,2,8)
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D
(3,6,13)
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Solution

The correct option is D (3,6,13)
Given line is x1=y4=z5
Line parallel to this and passing through P(1,2,3) is
x11=y+24=z35=λ (say)
Let the image be Q which lies on the line, so
Q(λ+1,4λ2,5λ+3)

Midpoint of P and Q is R(λ+22,4λ42,5λ+62)
Midpoint of P and Q lies on the plane 2x+3y4z+22=0
Putting it in the equation of plane, we get
λ+2+3(2λ2)2(5λ+6)+22=03λ+6=0λ=2Q(3,6,13)

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