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Question

If the image of the point P(1, -2, 3) in the plane 2x+3y-4z+22=0 measured parallel to the line x1=y4=z5 is Q, then PQ is equal to


A

35

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B

242

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C

42

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D

65

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Solution

The correct option is B

242


Any line parallel to x1=y4=z5 and passing through P(1, -2, 3) is

x11=y+24=z35=λ (say)
Any point on above line can be written as
(λ+1,4λ2,5λ+3). Coordinates of R are (λ+1,4λ2,5λ+3)Since, point R lies on the above plane.
2(λ+1)+3(4λ2)4(5λ+3)+22=0λ=1
So, point R is (2, 2, 8).
Now, PR=(21)2+(2+2)2+(83)2=42PQ=2PR=242


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