1.

Prove (by distances) that the three points (3, 2, 4), (5, 4, 6) and (9, 8, 10) are collinear.

2.

Show that the points (0, 7, 10), ( 1, 6, 6) and ( 4, 9, 6) form an isosceles right-angled triangle.

3.

Show that the triangle formed by the three points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.

4.

Show that the points (1, 3, 4), ( 1, 6, 10), ( 7, 4, 7) and ( 5, 1, 1) are the vertices of a rhombus.

5.

Show that the points (1, 2, 3), ( 1, 2, 1), (2, 3, 2) and (4, 7, 6) are the vertices of a parallelogram.

6.

Find the point equidistant from ( a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0).

7.

Find the locus of a point which moves so that the sum of its distances from the points ( a, 0, 0) and ( a, 0, 0) is constant (= 2 k).

8.

Find the locus of a point which moves so that its distance from (0, 0, 0) is twice its distance from ( 1, 2, 3).

9.

Find the ratio in which the XOY plane divides the join of the points ( 3, 4, 8) and (5, 6, 4) and thus write the coordinates of the...