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Question

If the line x23=y15=z+22 lies on the plane x+3yαz+β=0, then (α,β) equals .

A
(-5, -15)
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B
(-5, -15)
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C
(-6,7)
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D
(-6, -7)
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Solution

The correct option is C (-6,7)
DRs of line = (3, -5, 2)
DR's of normal to the plane = (1, 3, -α )
The line is perpendicular to the normal 3(1)5(3)+2(α)=03152α=02α=12α=6

Also (2, 1, -2) lies on the plane.
2+3+6(2)+β=0β=7
(α,β)=(6,7)

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