Class 12 Math: Three Dimensional Geometry Quick Revision Chapter Summary

Need to review the entire chapter before a test? This quick revision guide summarizes all the core concepts, topics, and equations taught in Class 12 Three Dimensional Geometry to help you refresh your memory instantly.

Core Topics At a Glance

### 📌 Direction cosines and direction ratios of a line The direction cosines (l, m, n) of a line are the cosines of the angles it makes with the coordinate axes. Direction ratios (a, b, c) are any numbers proportional to the direction cosines.

### 📌 Vector and Cartesian equations of a line in space A straight line in space can be defined by a point it passes through and its direction vector. It is represented in vector form or Cartesian form.

### 📌 Angle between two lines The angle θ between two lines in space is the angle between their direction vectors, calculated using the dot product of their directions.

### 📌 Shortest distance between two lines (skew lines) Skew lines are lines in space that are not parallel and do not intersect. The shortest distance between them is measured along their common perpendicular line.

### 📌 Distance of a point from a plane The perpendicular distance from a point P(x1, y1, z1) to a plane Ax + By + Cz + D = 0 is calculated using a standard coordinate formula.

Key Formulas Mind Map

• Line Vector Equation: `\vec{r} = \vec{a} + \lambda \vec{b}` - Vector form of line passing through a parallel to b....
• Shortest Distance Skew Lines: `d = \frac{|(\vec{b}_1 \times \vec{b}_2) \cdot (\vec{a}_2 - \vec{a}_1)|}{|\vec{b}_1 \times \vec{b}_2|}` - Distance between skew lines....

Revision Checklist

1. Review the subtopic guides and outline notes.
2. Practice writing the key formulas from memory.
3. Solve at least 3 worked examples and check your steps.
4. Take a timed practice quiz to verify your speed.