Question

The dc's (l,m,n) of two lines are connected between the relation l+m+n=0, lm=0, then the angle between the lines is

A
π3
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B
π4
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C
π2
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D
π6
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Solution

The correct option is A π3We know that,cosθ=−→b1.→b2−→|b1|∣∣∣→b2∣∣∣ ...... (1) Given that, l+m+n=0 l+m=−n −(l+m)=n And, lm=0 So,Either l=0 or m=0 When, l=0, then m=−n And, (l,m,n)=(0,1,−1) When, m=0, then l=−n And, (I,m,n)=(1,0,−1) Calculate b1⋅b2. b1.b2=(0,1,−1).(1,0,−1) =0+0+1 =1 Therefore,|b1|=√02+12+(−1)2=√2 |b2|=√02+12+(−1)2=√2 Now, substitute the values in equation (1). cosθ=→b1.→b2∣∣∣→b1∣∣∣∣∣∣→b2∣∣∣ ⇒cosθ=1√2.√2=12 ⇒θ=π3Hence, the angle between the lines is π3.

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