If the directions cosines of a line are k,k,k, then

If l₁, m₁, n₁; l₂, m₂, n₂; l₃, m₃, n₃ are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l₁ + l₂ + l₃, m₁ + m₂ + m₃, n₁ + n₂ + n₃ makes equal angles with them.

Distance of the point (α, β, γ) from y-axis is

The distance of the plane from the origin is

The sine of the angle between the straight lineand the plane 2x – 2y + z = 5 is