InterviewSolution
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InterviewSolution
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Three lines `px+qy+r=0`, `qx+ry+p=0` and `rx+py+q=0` are concurrent , ifA. `p+q+r=0`B. `p^(2)+q^(2)+r^(2)=pr+rq`C. `p^(3)+q^(3)+r^(3)=3pqr`D. None of these |
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Answer» Given lines `px+qy+r=0`, `qx+ry+p=0` and `rx+py+q=0` are concurrent. `:. |{:(p,q,r),(q,r,p),(r,p,q):}|=0` Applying `R_(1) to R_(1)+R_(2)+R_(3)` and taking common from `R_(1)` `(p+q+r)|{:(1,1,1),(q,r,p),(r,p,q):}|=0` `implies(p+q+r)(p^(2)+q^(2)+r^(2)-pq-qr-pr)=0` `implies p^(3)+q^(3)+r^(3)-3pqr=0` Therefore, `(a)` and `(c )` are the answers. |
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