Three lines `px+qy+r=0`, `qx+ry+p=0` and `rx+py+q=0` are concurrent , if
A. `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
A. `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
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.