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Question

If the direction ratios of two lines given by l+2m+3n=0 and 3lm+mn4nl=0, then angle between the lines is

A
π2
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B
π3
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C
π4
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D
π6
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Solution

The correct option is A π2
Given, l+2m+3n=0, 3lm+mn4nl=0

l(3m4n)+mn=0

(2m+3n)(4n3m)+mn=0

8mn6m2+12n29mn+mn=0

12n2=6m2

m=±2

The corresponding values of l will be (3+22)n and (322)n

Hence, the direction ratios will be

(2,1,(3+22)) and

(2,1,(322))

Taking dot product, we get

2+1+(98)

=1+98 =0

Hence, θ=π2

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