## CBSE Class 11 Maths Notes Chapter 12 Introduction to Three Dimensional Geometry

**Coordinate Axes**

In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are three mutually perpendicular lines. These axes are called the X, Y and Z axes.

**Coordinate Planes**

The three planes determined by the pair of axes are the coordinate planes. These planes are called XY, YZ and ZX plane and they divide the space into eight regions known as octants.

**Coordinates of a Point in Space**

The coordinates of a point in the space are the perpendicular distances from P on three mutually perpendicular coordinate planes YZ, ZX, and XY respectively. The coordinates of a point P are written in the form of triplet like (x, y, z).

The coordinates of any point on

- X-axis is of the form (x, 0,0)
- Y-axis is of the form (0, y, 0)
- Z-axis is of the form (0, 0, z)
- XY-plane are of the form (x, y, 0)
- YZ-plane is of the form (0, y, z)
- ZX-plane are of the form (x, 0, z)

**Distance Formula**

The distance between two points P(x_{1}, y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) is given by

The distance of a point P(x, y, z) from the origin O(0, 0, 0) is given by

OP = \(\sqrt { { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } }\)

**Section Formula**

The coordinates of the point R which divides the line segment joining two points P(x_{1}, y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) internally or externally in the ratio m : n are given by

The coordinates of the mid-point of the line segment joining two points P(x_{1}, y_{1}, z_{1}) and Q(x_{2}, y_{2}, z_{2}) are

The coordinates of the centroid of the triangle, whose vertices are (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}) and (x_{3}, y_{3}, z_{3}) are

### Maths Notes For Class 11 PDF Free Download Chapterwise

- Chapter 1 Sets Class 11 Notes
- Chapter 2 Relations and Functions Class 11 Notes
- Chapter 3 Trigonometric Functions Class 11 Notes
- Chapter 4 Principle of Mathematical Induction Class 11 Notes
- Chapter 5 Complex Numbers and Quadratic Equations Class 11 Notes
- Chapter 6 Linear Inequalities Class 11 Notes
- Chapter 7 Permutations and Combinations Class 11 Notes
- Chapter 8 Binomial Theorem Class 11 Notes
- Chapter 9 Sequences and Series Class 11 Notes
- Chapter 10 Straight Lines Class 11 Notes
- Chapter 11 Conic Sections Class 11 Notes
- Chapter 12 Introduction to Three Dimensional Geometry Class 11 Notes
- Chapter 13 Limits and Derivatives Class 11 Notes
- Chapter 14 Mathematical Reasoning Class 11 Notes
- Chapter 15 Statistics Class 11 Notes
- Chapter 16 Probability Class 11 Notes