If `vec(a)`and `vec(b)` are two non-collinear vectors, show that points `l_(1)vec(a)+m_(1)vec(b),l_(2)vec(a)+m_(2)vec(b)` and `l_(3)vec(a)+m_(3)vec(b)` are collinear if `|{:(l_(1),l_(2),l_(3)),(m_(1),m_(2),m_(3)),(1,1,1):}|=0` .

Answer

`=>|{:(l_(1),l_(2),l_(3)),(m_(1),m_(2),m_(3)),(1,1,1):}|=0`