Introduction to Three Dimensional Geometry – Class 11 Maths (NCERT Based)
The chapter Introduction to Three Dimensional Geometry introduces students to geometry in space, extending concepts from the 2D plane to three dimensions. This chapter forms the foundation for vector geometry, 3D coordinate geometry, and calculus in space.
This guide is strictly NCERT-aligned and written in a student-friendly manner.
📖 Coordinates in 3D Space
A point P in 3D space is represented as:
P(x, y, z)
- x, y, z are distances from the three mutually perpendicular axes (x-axis, y-axis, z-axis).
- The axes intersect at the origin O(0, 0, 0).
🔹 Distance Formula in 3D
Distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂):
PQ = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]
🔹 Section Formula in 3D
Coordinates of a point R dividing the line segment PQ in the ratio m:n:
R = ((nx₁ + mx₂)/(m + n), (ny₁ + my₂)/(m + n), (nz₁ + mz₂)/(m + n))
🔹 Midpoint Formula
Midpoint M of line segment joining P(x₁, y₁, z₁) and Q(x₂, y₂, z₂):
M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)
🔹 Coordinate Planes in 3D
- xy-plane: z = 0
- yz-plane: x = 0
- zx-plane: y = 0
Distance of a point from the coordinate planes:
- Distance from xy-plane = |z|
- Distance from yz-plane = |x|
- Distance from zx-plane = |y|
🔹 Distance from Origin
For a point P(x, y, z), the distance from the origin:
OP = √(x² + y² + z²)