1.

If (a, b), (c, d) and (a-c, b-d) are collinear, then which one of the following is correct ?A. `bc-ad=0`B. `ab-cd=0`C. `bc+ad=0`D. `ab+cd=0`

Answer» Correct Answer - A
Let A, B and C having co-ordinates (a, b), (c, d) and `{(a-c), (b-d)}` respectively be the points
If these points are collinear then
`|(a,b,1),(c,d,1),(a-c,b-d,1)|=0`
`R_(2) rarr R_(2)-R_(1)` gives
`|(a,b,1),(c-a,d-b,0),(a-c,b-d,1)|=0`
`R_(3) rarr R_(2)+R_(3)` gives
`|(a,b,1),(c-a,d-b,0),(0,0,1)|=0`
`implies 1. {a(d-b)-b(c-a)}=0`
`implies ad-ab-bc+ab=0`
`implies bc-ad=0`


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