Show that the three points A (2, 3, 4), B (−1, 2, −3) and C (−4, 1, −10) are collinear and find the ratio in which C divides AB.
2:1 externally
The mid-point of the sides of a triangle are (1, 5, −1), (0, 4, −2) and (2, 3, 4). Find its vertices. Also find the centroid of the triangle.
vertices are (3,4,5), (−1,6,−7), (1,2,3) and centroid is (1,4, 1/3)
Prove that the points (0, −1, −7), (2, 1, −9) and (6, 5, −13) are collinear. Find the ratio in which the first point divides the join of the other two.
1:3 externally
What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin coincide with the positive direction of the axes through the origin?
(2,0,0), (2,2,0), (0,2,0), (0,2,2), (2,0,2), (0,0,0), (2,2,2)