Class 12 Mathematics Chapter 11 Three-Dimensional Geometry – Revision Notes

Quick revision notes for Class 12 Maths Chapter 11 (Three-Dimensional Geometry). These Class 12 Mathematics Chapter 11 notes are ideal for quick revision just before exams.

Direction Cosines/Ratios

• l²+m²+n²=1.
• Parallel lines: a₁/a₂=b₁/b₂=c₁/c₂. Perpendicular: a₁a₂+b₁b₂+c₁c₂=0.

Lines & Planes

• Line: r=a+λb; Cartesian (x−x₁)/a=(y−y₁)/b=(z−z₁)/c.
• Plane: r·n=d; Cartesian ax+by+cz=d.

Distances

• Point to plane: |ax₁+by₁+cz₁−d|/√(a²+b²+c²).
• Skew lines: scalar triple product formula.

One-Line Summary

3D Geometry extends vectors to describe lines and planes in space using direction cosines/ratios, with distance and angle formulas built from dot and cross products.

Written by Satish

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