Question

show that the points with position vector a vector-2b vector+3c vector, -2a vector+3b vector-c vector and 4a vector - 7b vector + 7c vector are collinear??​

Answer 1

Step-by-step explanation:

Let A, B, C be the given points respectively

vector OA = -2a + 3b + 5c,

vector OB = a + 2b + 3c,

vector OC = 7a - c

vector AB = vector OB - vector OA 

= (a + 2b + 3c) - ( -2a + 3b + 5c) 

= 3a - b - 2c

vector AC = vector OC - vector OA 

= (7a - c) - ( -2a + 3b + 5c)

= 9a - 3b - 6c

= 3(3a - b - 2c)

= 3AB

⇒ Hence, AB,AC are collinear

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