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Question -

If the lines p1x + q1y = 1, p2x + q2y= 1 and p3x + q3y = 1 be concurrent, show that the points(p1, q1), (p2, q2) and (p3,q3) are collinear.



Answer -

Given:

p1x + q1y= 1

p2x + q2y= 1

p3x + q3y= 1

The given lines can bewritten as follows:

p1 x +q1 y – 1 = 0 … (1)

p2 x +q2 y – 1 = 0 … (2)

p3 x +q3 y – 1 = 0 … (3)

It is given that thethree lines are concurrent.

Now, consider thefollowing determinant:

Hence proved, thegiven three points, (p1, q1), (p2, q2)and (p3, q3) are collinear.

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