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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
12
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B
2
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C
0
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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
Given: xλ3=y12+λ=z31
So, the fixed point of the line (λ,1,3) must lie in the plane. Also the product of DR's of line and plane will be zero.
Condition I
Putting (λ,1,3) in the plane
We get λ2×1=0
λ=2(i)
Condition II
Product of DR's of line and plane
1(3)2(2+λ)+0(1)=0
342λ
λ=12(ii)
From (i) and (ii) we obtain different values of λ.
Hence, there is no such value of λ for which the line lies on the plane.

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