Find the equation of the plane passing through (1, 2, 3) with normal vector 2i − j + 3k.

Define direction cosines and state the relation they satisfy.

Find the angle between the line with direction ratios 1, 1, 2 and the plane x + y + z = 5.

Find the distance of the point (1, 2, 3) from the plane 2x − y + 2z − 9 = 0.

Find the angle between the planes 2x + y − 2z = 5 and 3x − 6y − 2z = 7.

If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.

Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.