Class 11 Mathematics — Chapter 11: INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

What you'll learn

• ▸Three-Dimensional Coordinate System
• ▸Coordinates of a Point in Space
• ▸Octants and Signs of Coordinates
• ▸Points on Axes and Planes
• ▸Distance Formula in Three Dimensions
• ▸Application of Distance Formula: Collinearity
• ▸Application of Distance Formula: Geometric Shapes
• ▸Equation of a Set of Points (Locus)

Chapter Summary

--- PAGE 1 --- Chapter 11 INTRODUCTION TO THREE DIMENSIONAL GEOMETRY ❖ *Mathematics is both the queen and the hand-maiden of all sciences – E.T. BELL* ❖ **11.1 Introduction** You may recall that to locate the position of a point in a plane, we need two intersecting mutually perpendicular lines in the plane. These lines are called the *coordinate axes* and the two numbers are called the *coordinates* of the point with respect to the *axes*. In actual life, we do not have to deal with points lying in a plane only. For example, consider the position of a ball thrown in space at different points of time or the position of an aeroplane as it flies from one place to another at different times during its flight. Similarly, if we were to locate the position of the lowest tip of an electric bulb hanging from the ceiling of a room or the position of the central tip of the ceiling fan in a room, we will not only require the perpendicular distances of the point to be located from two perpen…

Practice Questions from this Chapter

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1. Show 3D geometry in daily life. Get Solution →
2. Explain coordinate systems simply. Get Solution →
3. Visualize octants in a room. Get Solution →
4. What are the three mutually perpendicular lines X'OX, Y'OY, and Z'OZ called in a three-dimensional space? Get Solution →
5. What are the coordinates of the origin O in a three-dimensional coordinate system? Get Solution →
6. The three coordinate planes divide the space into how many parts? Get Solution →
7. What is the general form of the coordinates for any point on the x-axis? Get Solution →
8. If a point lies in the XZ-plane, what must its y-coordinate be? Get Solution →

Did you know?

• 💡 Our universe might actually have ten or more hidden spatial dimensions.
• 💡 Chameleons move each eye separately to achieve a full 360-degree 3D view.
• 💡 GPS systems pinpoint locations on Earth using extremely accurate three-dimensional coordinates.
• 💡 Ancient Egyptians designed their massive pyramids using advanced 3D geometric principles.
• 💡 A tesseract is a four-dimensional cube, impossible for humans to fully visualize.

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