1 A 1 B 1 C 1 D 1 E 2 3 4 5 6 7 8 9 10

RD Sharma - Mathematics

23. The Straight Lines

1. Sets
2. Relations
3. Functions
4. Measurement of Angles
5. Trigonometric Functions
6. Graphs of Trigonometric Functions
7. Values of Trigonometric Functions at Sum of Difference of Angles
8. Transformation Formulae
9. Values of Trigonometric Functions at Multiples and Submultiple of an Angles
10. Sine and Cosine Formulae and their Applications
11. Trigonometric Equations
12. Mathematical Induction
13. Complex Numbers
14. Quadratic Equations
15. Linear Inequations
16. Permutations
17. Combinations
18. Binomial Theorem
19. Arithmetic Progressions
20. Geometric Progressions
21. Some Special Series
22. Brief Review of Cartesian System of Rectangular Co-ordinates
23. The Straight Lines
24. The Circle
25. Parabola
26. Ellipse
27. Hyperbola
28. Introduction to 3-D Coordinate Geometry
29. Limits
30. Derivatives
31. Mathematical Reasoning
32. Statistics
33. Probability

Exercise 23.1

1 A 1 B 1 C 1 D 2 A 2 B 2 C 3 A 3 B 3 C 3 D 4 5 A 5 B 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Exercise 23.2

Exercise 23.3

1 2 3 4 5 6 7 8

Exercise 23.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.5

1 A 1 B 1 C 1 D 1 E 1 F 2 A 2 B 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.6

1 A 1 B 2 3 A 3 B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Exercise 23.7

1 A 1 B 1 C 1 D 2 3 4 5 6 7 8 9 10

Exercise 23.8

1 2 3 4 5 6 7 8 9 10 11 12 13

Exercise 23.9

1 2 A 2 B 2 C 2 D 2 E 3 4 5 6 7 8

Exercise 23.10

1 A 1 B 1 C 2 A 2 B 3 A 3 B 3 C 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Exercise 23.11

1 A 1 B 1 C 2 3 4 5 6 7 8

Exercise 23.12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Exercise 23.13

1 A 1 B 1 C 1 D 1 E 2 3 4 5 6 7 8 9 10

Exercise 23.14

Exercise 23.15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Exercise 23.16

1 A 1 B 1 C 1 D 2 3 4 5 6

Exercise 23.17

Exercise 23.18

1 2 3 4 5 6 7 8 9 10 11 12 13

Exercise 23.19

1 2 3 4 5 6 7 8 9 10 11

Very Short Answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

MCQ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Q. 1 C5.0( 1 Vote )

Find the angles between each of the following pairs of straight lines :

3x + 4y – 7 = 0 and 4x – 3y + 5 = 0

Class 11th RD Sharma - Mathematics 23. The Straight Lines

Answer :

Given:

The equations of the lines are

3x + 4y − 7 = 0 … (1)

4x − 3y + 5 = 0 … (2)

To find:

Angles between two lines.

Explanation:

Let m₁ and m₂ be the slopes of these lines.

m₁m₂

∵m₁m₂

Hence, the given lines are perpendicular.
Therefore, the angle between them is 90°.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSFind the angles between each of the following pairs of straight lines :3x – y + 5 = 0 and x – 3y + 1 = 0 NEXTFind the angles between each of the following pairs of straight lines :x – 4y = 3 and 6x – y = 11

Related Videos

Various Forms of Equations of lineFREE Class

Parametric Equations of Straight line48 mins

Straight line | Analyse your learning through quiz56 mins

General Equation of a lineFREE Class

Slope, inclination and angle between two lines48 mins

Interactive Quiz on Equations of lineFREE Class

Motion in a Straight Line - 0665 mins

Motion in a Straight Line - 0556 mins

Motion in a Straight Line - 0372 mins

Motion in a Straight Line - 1063 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

view all courses