Step-by-step explanation:
If the vector CD is a multiple of the vector BC
(CD = kBC, where k is a real constant
and k =/= 0),
Then BCD is a straight line.
Vector BC = Vector BA - Vector CA
= (5a - 2b) - (3a + b) = (2a - 3b).
Vector CD = Vector CA + Vector AD
= (3a + b) + (3a - 10b) = (6a - 9b)
Since 3(2a - 3b) = (6a - 9b), => k = 3,
The points B, C and D are collinear.
Hence we conclude BCD is a straight line.
