Introduction to Three Dimensional Geometry

Maths · Class 11

Simulation · Maths · Class 11

Which octant is P in?

"Which octant is P in?" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "The eight octants" in Introduction to Three Dimensional Geometry. Pick x, y or z and move its slider. P is reached in three steps: x along the x-axis (red), then y parallel to the y-axis (green), then z straight up or down (blue). Watch the octant name change when a sign flips. The signs of (x, y, z) name the octant: I to IV have z positive, and V to VIII sit directly below them with z negative. A zero coordinate puts the point on a coordinate plane, and two zeros put it on an axis.

From the lesson The eight octants in Introduction to Three Dimensional Geometry. Change the values and watch what happens.

Which octant is P in?Maths · Class 11

The idea behind it

NCERT §11.2, Table 11.1

  • The three coordinate planes split the whole of space into eight parts called octants, just as the two axes split the plane into four quadrants.
  • Each is named by the three half-axes that bound it and numbered I to VIII: I is XOYZ, II is X′OYZ, III is X′OY′Z, IV is XOY′Z, V is XOYZ′, VI is X′OYZ′, VII is X′OY′Z′ and VIII is XOY′Z′.
  • Octants I to IV lie above the XY-plane (z positive) and V to VIII below it (z negative). Each lower octant sits directly under the upper one with the same number minus four: V under I, VI under II, VII under III, VIII under IV.
  • Signs of (x, y, z): I (+, +, +), II (−, +, +), III (−, −, +), IV (+, −, +), V (+, +, −), VI (−, +, −), VII (−, −, −), VIII (+, −, −).
  • So the signs alone name the octant: (−3, 1, 2) is in octant II and (−3, 1, −2) is in octant VI. Likewise (2, −5, 4) is in IV and (−1, −1, −1) is in VII.
  • A point with a zero coordinate lies on a coordinate plane and belongs to no octant.

Questions

2 answers

What does the "Which octant is P in?" simulation show?
Pick x, y or z and move its slider. P is reached in three steps: x along the x-axis (red), then y parallel to the y-axis (green), then z straight up or down (blue). Watch the octant name change when a sign flips.
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "The eight octants" in Introduction to Three Dimensional Geometry (Class 11 Maths).

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