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Question

The value of λ for which the straight line xλ3=y12+λ=z31 may lie on the plane x2y=0, is

A
2
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B
0
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C
12
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D
there is no such λ
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Solution

The correct option is D there is no such λ
If a line xx1a1=yy1b1=zz1c1 lies on a plane a2x+b2y+czz=d, then
i) a1a2+b1b2+c1c2=0
ii) a2x1+b2y1+c2z1=d
According to the question,
3(1)+(2+λ)(2)+(1)(0)=0
342λ=0
λ=1/2
Also, λ2=0
λ=2
So, there is no such value of λ.

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