Chapter Overview
The chapter 'Three-Dimensional Geometry' provides tools to analyze and interpret geometric figures in 3D space. Students learn about direction cosines and direction ratios of a line, equations of a line and a plane, and angles between lines, planes, and a line and a plane. This chapter extends two-dimensional coordinate geometry into three-dimensional space, which is essential in fields such as physics, engineering, and computer graphics.
Important Keywords
- Direction Cosines (d.c.s): Cosines of angles made by a line with x, y, and z axes.
- Direction Ratios (d.r.s): A set of three numbers proportional to the direction cosines of a line.
- Line Equation (Vector Form): r = a + λb, where a is a position vector and b is direction vector.
- Plane Equation: ax + by + cz + d = 0 is the Cartesian form.
- Angle between Lines: Determined using dot product of direction vectors.
- Skew Lines: Non-parallel and non-intersecting lines in space.
Detailed Notes
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