To prove: the 3 points are collinear.
Formula: The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)
Here,
(x1,y1,z1) = (3, -5, 1)
(x2,y2,z2) = (-1, 0, 8)
(x3,y3,z3) = (7, -10, -6)
Length AB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)
Length AC = \(\sqrt{(x_3-x_1)^2+(y_3-y_1)^2+(z_3-z_1)^2}\)
Therefore A,B,C are collinear.