Find the distance from the origin to (6, 6, 7).

Let A, B, C be the feet of perpendiculars from a point P on the xy, yz and zxplanes respectively. Find the coordinates of A, B, C in each of the following where the point P is

(i) (3, 4, 5) (ii) (–5, 3, 7) (iii) (4, – 3, – 5).

How far apart are the points (2, 0, 0) and (–3, 0, 0)?

Show that if x² + y² = 1, then the point is at a distance 1 unit from the origin.

Show that the point A (1, – 1, 3), B (2, – 4, 5) and (5, – 13, 11) are collinear.