NCERT Solutions For Class 11 Maths Chapter 10: Straight Lines

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NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines are provided in the article below. A straight line is a distance covered by a point moving in a steady direction with zero curvature. The basic ideas of lines, such as slopes, angles between two lines, different types of lines, and distance between lines, are covered in Class 11 Maths NCERT Solutions Chapter 10 Straight Lines.

Download: NCERT Solutions for Class 11 Mathematics Chapter 10 pdf

Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

Class 11 Maths NCERT Solutions Chapter 10 Straight Lines are provided below:

Also check: Concept Notes on Straight Lines

Important Topics: Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

Important Topics Class 11 Maths NCERT Solutions Chapter 10 Straight Lines are elaborated below:

Slopes

Slope of the line is the ratio of the rise to the run, or rise divided by the run. It shows the steepness of a line in coordinate plane.

Example: What is the equation of a line whose slope is 1, and that passes through the point (-1, -5)?

Solution: If the slope is given as 1, then the value of m will be 1 in the general equation y = mx + b. Thus, we substitute value of m as 1, and we get,

y = x + b

Now, value of one point on the line is already provided. Thus, we will put the value of the point (-1, -5) in the equation y = x + b, and we will get, b = -4.

Therefore, substituting values of m and b in the general equation, the final equation is y = x - 4.

Angles between Two Lines

Angle between two lines helps to know the relationship between the two lines. It is the measure of the inclination between the two lines.

How to Calculate Angle Between Two Lines:

Consider three points given on the x-axis and y-axis whose coordinates are provided.
A line whose endpoints have coordinates (x1 y1) and (x2 y2).
The equation of the slope will be: m = y₂ - y₁/x₂ - x₁
Thus, m1 and m2 can be calculated by substituting this in the above formula:
tan θ = ± (m₁ - m₂ ) / (1- m₁*m₂)

Types of Lines

In Geometry, there are four types of lines:

Horizontal Lines: A horizontal line moves from left to right in a straight direction.
Vertical Lines: A vertical line moves from top to bottom in a straight direction
Parallel Lines: Parallel lines are two straight lines that don’t meet or intersect at any point, even at infinity.
Perpendicular Lines: Perpendicular lines are two lines that meet or intersect at an angle of 90 degrees or at a right angle.

NCERT Solutions For Class 11 Maths Chapter 10 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 10 Straight Lines under different exercises are as follows:

Also check:

Chapter Related Topics
Horizontal and vertical lines	Analytical Geometry	Intercept
Slope Formula	Slope Intercept Form Formula	Point Gradient Formula
Perpendicular Line Formula	Point Slope Form Formula	Different Forms of Equation of Line

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

View Solution

2.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

View Solution

3.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

\(x^4+\frac{1}{x^3}-\frac{129}{8}\)
\(x^3+\frac{1}{x^4}+\frac{129}{8}\)
\(x^4+\frac{1}{x^3}+\frac{129}{8}\)
\(x^3+\frac{1}{x^4}-\frac{129}{8}\)

View Solution

4.
Find the following integral: \(\int (ax^2+bx+c)dx\)

View Solution

5.
Solve system of linear equations, using matrix method.
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

View Solution

6.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

View Solution

View All

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Straight Line: Type, Properties & Examples

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Point Slope Form Formula: Equation of Straight Line & Solved Questions

Area Under the Curve Formula & Solved Questions

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NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.1

NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.2

NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.3

NCERT Solutions for Class 11 Maths Chapter 10 Miscellaneous Exercises

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NCERT Solutions For Class 11 Maths Chapter 10: Straight Lines

Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

Important Topics: Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

NCERT Solutions For Class 11 Maths Chapter 10 Exercises:

CBSE CLASS XII Related Questions

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

3.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

4.
Find the following integral: \(\int (ax^2+bx+c)dx\)

5.
Solve system of linear equations, using matrix method.
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

6.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

Similar Mathematics Concepts

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NCERT Solutions For Class 11 Maths Chapter 10: Straight Lines

Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

Important Topics: Class 11 Maths NCERT Solutions Chapter 10 Straight Lines

NCERT Solutions For Class 11 Maths Chapter 10 Exercises:

CBSE CLASS XII Related Questions

1. Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2. If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

3. If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

4. Find the following integral: \(\int (ax^2+bx+c)dx\)

5. Solve system of linear equations, using matrix method. x-y+2z=7 3x+4y-5z=-5 2x-y+3z=12

6. Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

3.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

4.
Find the following integral: \(\int (ax^2+bx+c)dx\)

5.
Solve system of linear equations, using matrix method.
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

6.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)