Find the centroid of the triangle whose vertices are (1, 2, 3), (4, 5, 6) and (7, 8, 9).

Find the coordinates of the point dividing the join of (2, 3, 4) and (8, 9, 10) in the ratio 1 : 2 internally.

A line makes equal angles with all three coordinate axes. Find its direction cosines.

Find the distance between the points (1, 2, 3) and (4, 6, 3).

Name the eight octants of three-dimensional space and state the signs of the coordinates in the first octant.

In a class of 60 students, 35 play cricket, 28 play football and 12 play both. How many play neither?

Prove that cos 2A = 1 − 2sin²A.