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Question

Find the angles between the lines, whose direction cosines are give by the equation l2m2+n2=0,l+m+n=0

A
0
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B
π6
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C
π4
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D
π3
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Solution

The correct option is D π3

Lines are l+m+n=0l=(m+n)

and l2m2+n2=0l2=m2n2

Solving them gives,

((m+n))2=m2+n2+2mn=m2n22n(n+m)=0

Now, For n=0

m=l, so d.c's (12,12,0)

And for n=m

l=0 so d.c's (0,12,12)

Angle between the lines |cosθ|=12θ=π3


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