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Question

If θ the angle between the line x+11=y12=z22 and the plane 2xy+λz+4=0 is such that sinθ=13. then the value λ is

A
43
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B
34
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C
35
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D
53
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Solution

The correct option is D 53
Given, equation of line x+11=y12=z22 for which a1=1,b1=2,c1=2 and the plane 2xy+λz+4=0 for which a2=2,b2=1 and c2=λ.
Now, given sinθ=13
Therefore, sinθ=∣ ∣ ∣a1a2+b1b2+c1c2a21+b21+c21a22+b22+c22∣ ∣ ∣
13=22+2λ1+4+44+1+λ
13=2λ95+λ
5+λ=2λ
5+λ=4λ
3λ=5
λ=53

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