Chapter 11 · Class XI Mathematics · NCERT Exercises

Introduction to 3D Geometry — Exercises

Step Into Space — All 3D Coordinate Geometry Exercises Solved

📂 3 Exercises 📝 15 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

3D axes; octants; locating points in space

3D distance; section formula; midpoint; centroid

Collinearity in 3D; distance from axes and planes

3 exercise files · 15 total questions

Chapter at a Glance

JEE MainJEE AdvancedCBSE BoardsBITSAT

8Concepts

10Formulas

ModerateDifficulty

4–5%Weightage

Before You Begin

Prerequisites

✓2D coordinate geometry (Class X)
✓Distance formula in 2D
✓Section formula in 2D

Have Ready

🔧3D axis reference diagram
🔧Scientific calculator

Exercise Topic Map

Exercise 11.1Name octant from sign of (x,y,z); identify points on axes/planes

Exercise 11.2d=√[Σ(Δcoord)²]; section formula in 3D; midpoint; centroid G

MiscellaneousCollinearity (ratio check); distance from coordinate planes

Key Formulae

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

\(P = \!\left(\tfrac{mx_2+nx_1}{m+n},\tfrac{my_2+ny_1}{m+n},\tfrac{mz_2+nz_1}{m+n}\right)\)

\(G = \!\left(\tfrac{x_1+x_2+x_3}{3},\tfrac{y_1+y_2+y_3}{3},\tfrac{z_1+z_2+z_3}{3}\right)\)

\(\text{Distance from XY-plane} = |z|\)

NCERT Solving Method

Step 1 — All 2D formulas extend to 3D by adding the z-term — one pattern covers everything. Step 2 — Octants: list signs of (x,y,z); 8 sign combos = 8 octants. Step 3 — Section: internal (point between) uses +; external (point outside) uses − in numerator. Step 4 — Collinearity: check if ratio m:n is same for all three coordinates.

Continue Your Preparation

📖 Notes Theory & concepts 🧠 MCQs Topic-wise practice 🎯 PYQs JEE · CBSE · BITSAT ⚖️ True–False Topic-wise concept check ➡️ Next Chapter Limits & Derivatives

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