Currently Empty: $0.00
8.Direction Cosines & Ratios
Class 11 • Mathematics • NCERT
3D Geometry – Distance Formula
[ Embed Your Video Lecture Here ]
This lesson introduces distance calculation between two points in three-dimensional space as per NCERT Class 11. Students learn the 3D distance formula and understand how it extends the 2D distance concept.
Lesson Objectives
- Understand coordinates in 3D space.
- Learn the distance formula in three dimensions.
- Relate 3D distance with 2D distance.
- Solve simple NCERT-style problems.
1. Three-Dimensional Coordinate System
In three-dimensional geometry, the position of a point is represented using three coordinates.
• x-coordinate → distance along x-axis
• y-coordinate → distance along y-axis
• z-coordinate → distance along z-axis
• y-coordinate → distance along y-axis
• z-coordinate → distance along z-axis
2. Coordinates of a Point in 3D
A point in three-dimensional space is written as an ordered triplet.
P(x, y, z)
3. Distance Formula in 3D
The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by:
Distance = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]
4. Relation with 2D Distance Formula
If the z-coordinates of both points are zero, the 3D distance formula reduces to the 2D distance formula.
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
5. Simple NCERT Examples
• Find the distance between A(1,2,3) and B(4,6,3)
Distance = √[(3)² + (4)² + (0)²] = 5
Distance = √[(3)² + (4)² + (0)²] = 5
Practice Questions (NCERT)
- What is a 3D coordinate system?
- How many coordinates are needed to locate a point in space?
- Write the general form of a point in 3D.
- State the distance formula in 3D.
- Find the distance between (0,0,0) and (1,2,2).
- What happens when z₁ = z₂ = 0?
- Can distance be negative?
- What shape does distance represent?
- Is the distance formula symmetric?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- A system to locate points using three coordinates.
- Three
- (x, y, z)
- √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]
- 3
- Becomes 2D distance formula
- No
- Straight-line distance
- Yes
- Yes
© Aviate Learning – 3D Geometry (NCERT Class 11)