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Questions and Answers
What do direction ratios (DRs) represent in mathematics?
How can direction cosines (DCs) be found?
What is the condition for two lines to be considered parallel?
What defines the angle between two lines based on their direction ratios?
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Which of the following statements about direction ratios and lines is incorrect?
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Study Notes
Direction Ratios
- Direction ratios (DRs) are a set of numbers (a,b,c) that describe the direction of a line in space.
- DRs can be determined for a line given different information, including points on the line.
- Formulas exist for calculating DRs.
Direction Cosines
- Direction cosines (DCs) are cosines of the angles that a line makes with the x, y, and z axes.
- DCs can be calculated from direction ratios and vice-versa.
Angle Between Two Lines
- The angle between two lines can be found using their direction ratios.
- Formulas exist for calculating the angle between lines using DRs.
Parallel and Perpendicular Lines
- Lines are parallel if their direction ratios are proportional ($l_1 || l_2$).
- Lines are perpendicular if the dot product of their direction ratios is zero (l1 $ \perp$ l2).
Equations of Lines
- Equations of lines can be derived using coordinate geometry formulas.
- Equations can be found given two points or a point and direction ratios.
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Description
This quiz covers the essential concepts of direction ratios and direction cosines in three-dimensional geometry. You will explore how to calculate direction ratios from given points, the relationship between direction ratios and angles, and the conditions for lines to be parallel or perpendicular. Additionally, you'll learn about the equations of lines in 3D space.
