In the following cases, find the distance of each of the given points from the corresponding given plane.

Point Plane

(–6, 0, 0) 2x – 3y + 6z – 2 = 0

In the following cases, find the distance of each of the given points from the corresponding given plane.

Point Plane

(3, – 2, 1) 2x – y + 2z + 3 = 0

In the following cases, find the distance of each of the given points from the corresponding given plane.

Point Plane

(2, 3, – 5) x + 2y – 2z = 9

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, –1), (4, 3, –1).

If l₁, m₁, n₁ and l₂, m₂, n₂ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are (m₁n₂ - m₂n₁), (n₁l₂ - n₂l₁), (l₁m₂ - l₂m₁)