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Vector Equation for Straight Line

30. Three lin...

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

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p x + q y + r = 0

q x + r y + p = 0

r x + p y + q = 0

are concurrent if

p x + q y + r = 0, q x + r y + p = 0 a n d r x + p y + q = 0

are concurrent then

p x + q y + r = 0, q x + r y + p = 0

r x + p y + q = 0

are concurrent, then the value of

p + q + r

p, q, r

Q. Prove that the lines

(p - q) x + (q - r) y + (r - p) = 0

(q - r) x + (r - p) y + (p - q) = 0

(r - p) x + (p - q) y + (q - r) = 0

are concurrent.

Three lines $p x + q y + r = 0, q x + r y + p = 0$ and $r x + p y + q = 0$ are concurrent, if

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