Introduction To Three- Dimensional Geometry

Three mutually perpendicular lines

Three mutually perpendicular lines—X-axis, Y-axis, and Z-axis—intersect at the origin O(0,0,0). Any point P in space is represented by an ordered trip

The distance between two points P(x₁

The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by the formula: √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]. This is an extension of th

If a point R divides

If a point R divides the line segment joining P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) in the ratio l:m, then its coordinates are: - Internally: ((lx₂ + mx₁)/(

If a line makes angles α

If a line makes angles α, β, γ with the positive X, Y, and Z axes respectively, then cosα, cosβ, cosγ are its direction cosines (l, m, n). They satisf

The projection of a line segment

The projection of a line segment joining P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) on a line with direction cosines l, m, n is given by: l(x₂−x₁) + m(y₂−y₁) + n