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in 3D Coordinate Geometry by (55.0k points)
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Show that the following points are collinear : 

A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

1 Answer

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Best answer

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.

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