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Questions and Answers
What do direction ratios (DRs) represent in mathematics?
What do direction ratios (DRs) represent in mathematics?
- A set of numbers defining the direction of a line (correct)
- The area of a triangle in space
- The midpoint of a line segment
- The length of a line segment
How can direction cosines (DCs) be found?
How can direction cosines (DCs) be found?
- By determining the area of the triangle formed
- By calculating the parallelism of two lines
- Using the length of the line segments
- From the direction ratios or vice versa (correct)
What is the condition for two lines to be considered parallel?
What is the condition for two lines to be considered parallel?
- The direction cosines are not equal
- The angles formed by the lines are supplementary
- Their direction ratios are equal
- One line's direction ratio is a scalar multiple of the other (correct)
What defines the angle between two lines based on their direction ratios?
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?
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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