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Question

Let the line
x23=y15=z+22
lies in the plane x+3yαz+β=0. Then (α,β) equals


A

(6,17)

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B

(6,7)

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C

(5,15)

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D

(5,15)

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Solution

The correct option is B

(6,7)


Dr's of line = (3, -5, 2)
Dr's of normal to the plane = (1, 3, - α )
Line is perpendicular to 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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