Introduction to Three-Dimensional Geometry — Class 11 Mathematics

Core Concepts

A point in three-dimensional space is represented by (x,y,z). The coordinate planes are xy, yz and zx planes. Distance between P(x₁,y₁,z₁) and Q(x₂,y₂,z₂) is √[(x₂−x₁)²+(y₂−y₁)²+(z₂−z₁)²].

Worked Example

Distance between (1,2,3) and (4,6,3) is √(9+16+0)=5.

A point lies on the xy-plane when z=0; on the yz-plane when x=0; on the zx-plane when y=0.

Explained MCQs

1. The distance from (0,0,0) to (2,3,6) is 7.
2. A point on the yz-plane has x=0.
3. The origin is (0,0,0).

Practice

1. Find the distance between (2,−1,3) and (5,3,15).
2. Identify the coordinate plane containing (0,4,−2).