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Question

The angle between the line r=i+2j+3k+λ2i+3j+4kand the plane r . i+2j-2k=0 is


A

0°

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B

60°

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C

30°

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D

90°

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E

45°

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Solution

The correct option is A

0°


Find the angle between the line and plane.

Consider the given equation as,

r=i+2j+3k+λ2i+3j+4k

i+2j-2k=0

We know that the general form of vector equation

r=a+λbr.n=dsinθ=b.nbn

Let,

b=2i+3j+4kn=i+2j-2k

Then,

b.n=2i+3j+4ki+2j-2kb.n=2×1+3×2+4×-2b.n=2+6-8b.n=0

Therefore,

sinθ=0bnsinθ=0θ=sin-10θ=0°

Hence, the correct answer is Option A.


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