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Question

# The image of point P(1,−2,3) in the plane 2x+3y−4z+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 x−11=y+24=z−35=λ (say) Let the image be Q which lies on the line, so Q≡(λ+1,4λ−2,5λ+3) Midpoint of P and Q is R≡(λ+22,4λ−42,5λ+62) Midpoint of P and Q lies on the plane 2x+3y−4z+22=0 Putting it in the equation of plane, we get λ+2+3(2λ−2)−2(5λ+6)+22=0⇒−3λ+6=0⇒λ=2∴Q≡(3,6,13)

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