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Let the line (x - 2)/3 = (y - 1)/-5 = (z +2)/2 lie in the plane  x + 3y – αz + β = 0. Then (α, β) equals

(a) (–6, 7) 

(b) (5, –15)

(c) (–5, 5) 

(d) (6, –17)

1 Answer

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(a) : The line is (x - 2)/3 = (y - 1)/-5 = (z + 2)/2

The direction ratios of the line are (3, –5, 2).
As the line lies in the plane x + 3y – αz + β = 0,
we have (3)(1) + (–5)(3) + 2(–α) = 0
⇒ –12 – 2α = 0. \ α = –6
Again (2, 1, –2) lies on the plane
⇒ 2 + 3 + 2α + β = 0
β = –2α – 5 = 12 – 5 = 7
Hence (α, β) is (–6, 7).

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