if the points  A (a1 , b1) ,(a2 ,b2) and (a1 - a2 , b1- b2) are collinear , then show that a1 b2 =a2 b1.

Dear Student,
Please find below the solution to the asked query:

As, Aa1,b1, Ba2,b2 and Ca1-a2, b1-b2 are collinearSo,a1b11a2b21a1-a2b1-b21=0R1R1-R2a1-a2b1-b20a2b21a1-a2b1-b21=0R3R3-R1a1-a2b1-b20a2b21001=0Expanding along R3, we get0+0+1b2a1-a2-a2b1-b2=0a1b2-a2b2-a2b1+a2b2=0a1b2-a2b1=0a1b2=a2b1

Regards

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