Chapter 11
Three vertices of a parallelogram ABCD are A(3, - 1, 2), B (1, 2, - 4) and C (- 1, 1, 2). Find the coordinates of the fourth vertex.
Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).
If the origin is the centroid of the triangle PQR with vertices P (2 a, 2, 6), Q (- 4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.
If A and B be the points (3, 4, 5) and (-1, 3, -7), respectively, find the equation of the set of points P such that PA2 + PB 2 = k2, where k is a constant.