Question

Show that the position vector of the points are 2a+5b-4c,a+4b-3c,4a+7b-6c collinear​

Answer 1

Answer:

refer to the Attachment

Answer 2

$use \: \: AB+BC=AC$

Step-by-step explanation:

$Let, \: A = 2a + 5b - 4c, \: B = a + 4b - 3c, \: and \: \: C = 4a + 7b - 6c \\ then, \: \: AB = (a + 4b - 3c) - (2a + 5b - 4c) = - a - b + c \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: BC = (4a + 7b - 6c) - (a + 4b - 3c) = 3a + 3b - 3c \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: AC = (4a + 7b - 6c ) - (2a + 5b - 4c) = 2a + 2b - 2c \\ Now, \: \: AB+BC= \:(- a - b + c ) + (3a + 3b - 3c) \\ = 2 a+ 2b - 2 c= AC \\ we \: \: see \: \: that, \: AB+BC=AC \\ Hence \: \: the \: \: given \: \: points \: \: are \: \: collinear.$