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Question

The distance of the point (2, 1, – 2) from the line x12=y+11=z33 measured parallel to the plane x + 2y + z = 4 is

A
10
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B
20
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C
5
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D
30
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Solution

The correct option is D 30
Let direction ratios of PQ and a, b, c
x+11=y2=z13

Then, x2a=y1b=z+2c
(Let PQ = r)
Q (ar + 2, br + 1, cr – 2)
Which lie on x12=y+12=z33,thenar+212=br+1+12=cr233ar+12=br+22=cr53=λ(say)a=2λ1r,b=2λ2r,c=3λ+5r
Given, PQ is parallel to x + 2y +z = 4, then
a + 2b + c = 0
or 2λ1r+4λ4r+3λ+5r=03λ=0λ=0thena=1r,b=2r,c=5rQ=(1,1,3)PQ(21)2+(1+1)2+(3+2)2=30

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