We have to show that the three points are colinear , i.e. they all lie on the same line,
If we define a line which is having a parallel line to AB and the points A and B lie on it, if point C also satisfies the line then, the three points are colinear,
Given A(-2, 4, 7) and B(3, -6, -8), AB = 5i – 10j -15k
The points on the line AB with A on the line can be written as,
R = (-2, 4, 7) +a(5, -10, -15)
Let C = (-2+5a, 4-10a, 7-15a)
(1, -2, -2) = (-2+5a, 4-10a, 7-15a)
If a = 3/5, then L.H.S = R.H.S, thus
The point C lies on the line joining AB,
Hence, the three points are colinear.
