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.
(1, −2, 8)
Find the lengths of the medians of the triangle with vertices A(0, 0, 6), B(0, 4, 0) and C(6, 0, 0).
7, \(\sqrt{34}\), 7
If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(−4, 3b, −10) and R(8, 14, 2c), find the values of \(a\), \(b\) and \(c\).
\(a = -2\), \(b = -\dfrac{16}{3}\), \(c = 2\)
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 \(PA^2 + PB^2 = k^2\), where \(k\) is a constant.
\(x^2 + y^2 + z^2 - 2x - 7y + 2z = \dfrac{k^2 - 109}{2}\)