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Three lines px+qy+r=0, qx+ry+p=0 and rx+...

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

Text Solution

AI Generated Solution

To determine the condition under which the three lines \( px + qy + r = 0 \), \( qx + ry + p = 0 \), and \( rx + py + q = 0 \) are concurrent, we will use the concept of determinants. The lines are concurrent if the determinant of the coefficients of \( x \) and \( y \) is equal to zero. ### Step-by-Step Solution: 1. **Write the Coefficient Matrix**: The coefficients of the lines can be arranged in a matrix form as follows: \[ \begin{vmatrix} ...
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