Question

If three points A,B&C have position vectors (1,x,3),(3,4,7) and (y,-2,-5) respectively.If they are collinear find the values of x&y.

Answer 1

If three points A,B&C have position vectors (1,x,3),(3,4,7) and (y,-2,-5) respectively.If they are collinear find the values of x&y

Since A, B, C are collinear, direction vector of AB = direction vector of BC
=> direction of (3-1, 4-x, 7-3) = direction of (y-3, -2-4, -5-7)
=> direction of (2, 4-x, 4) = direction of (y-3, -6, -12)
=. k(2, 4-x,4) = (y-3, -6,-12) for some scalar k
=> 4k = -12 => k = -3
=> -3(2) = y-3 => -6= y-3=> y = -3
also -3(4-x) = -6=> -12+3x= -6=> 3x = 6 => x = 2
Answer: x = 2 and y = -3