The directions cosines of two lines are connected by relations l+m+n=0 and 4l is the harmonic mean between m and n then

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l1l2+m1m2+n1n2=32

l1l2+m1m2+n1n2=-32

l1l2+m1m2+n1n2=12

l1l2+m1m2+n1n2=-12

answer is B.

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Detailed Solution

l+m+n=04l=2mnm+n⇒2lm−mn+2ln=0by eliminating n, we get2lm2−lm−1=0⇒l1m1=1,l2m2=−12 and ⇒n1n2=−2∴l1l2+m1m2+n1n2=1−12−2=−32

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