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Question

If the image of the point P(1,2,3) in the plane, 2x+3y4z+22=0 measured parallel to the line; x1=y4=z5 is Q, then PQ is equal to

A
242
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B
42
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C
65
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D
35
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Solution

The correct option is A 242
Given that image of P (1 , -2, 3) in the plane 2x + 3y - 4z + 22 = 0 measured parallel to line x1=y4=z5 is Q .
Take a look at diagram for understanding better.
As PQ is parallel to x1=y4=z5, D.R's also remain same.
Line PQ passing through (1 , -2, 3) can be written as
x11=y(2)4=z35=λ (let) ----eq.1
Let A is point on the plane and midpoint of P & Q.
From eq.1, coordinates of A will be of form
A=(λ+1,4λ2,5λ+3)
As A lies on the plane 2x + 3y - 4z + 22 = 0
2(λ+1)+3(4λ2)4(5λ+3)+22=0
6λ=6λ=1
A=(2,2,8),P(1,2,3)
Now, PA =(21)2+(2(2))2+(83)2=1+16+25=42
As PA = AQ, [ image]
PQ = 2PA =242

1880767_1221378_ans_40ceace2ba014769a338a1926230bda3.png

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