JEE AdvancedStraight LineMedium
Question
The lines xp + qy + r = 0, qx + ry + p = 0 and rx + py + q = 0 are concurrent, if
Options
A.p + q + r = 0
B.p2 + q2 + r2 = pr + rq
C.p3 + q3 + r3 = 3pqr
D.None of these
Solution
Given lines px + qy + r = 0, qx + ry + p = 0
and rx + py + q = 0 are concurrent.
∴
Applying R1 → R1 + R2 + R3 and taking common from R1
⇒ (p + q + r)
⇒ ( p + q + r) ( p2 + q2 + r2 - pq - pr) = 0
⇒ p3 + q3 + r3 - 3pqr = 0
Therefore, (a) and (c) are the answers. ......(i)
and rx + py + q = 0 are concurrent.
∴
Applying R1 → R1 + R2 + R3 and taking common from R1
⇒ (p + q + r)
⇒ ( p + q + r) ( p2 + q2 + r2 - pq - pr) = 0
⇒ p3 + q3 + r3 - 3pqr = 0
Therefore, (a) and (c) are the answers. ......(i)
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