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Cheat sheet · JEE Preparation Mathematics

Introduction to Three Dimensional Geometry cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Mathematics

Cheat sheet

Class 11 · Chapter 11Introduction to Three Dimensional Geometry

Three axes split space into 8 octants.

1. Coordinates

  • Point (x, y, z); on x-axis (x, 0, 0); in the xy-plane (x, y, 0).
  • Signs give the octant: I is (+, +, +).

2. Distance

PQ=(x2−x1)2+(y2−y1)2+(z2−z1)2PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}

Collinear points: PQ + QR = PR.

3. Key Points

  • Distance from origin: √(x² + y² + z²).
  • Distance from x-axis: √(y² + z²).
  • Three coordinate planes: xy, yz, zx.
  • Equidistant problems: equate squared distances.

Remember: Octants | 3-D distance formula

Introduction to Three Dimensional Geometry: questions and notes

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