NCERT Solutions For Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry

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NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry are given in the article. Class 11 Maths NCERT Solutions cover following key concepts: Cartesian Coordinate System and Distance between Two Points.

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Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry

Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry are provided below:

NCERT Solution

Also check: Concept Notes on Three Dimensional Geometry

Important Topics: Class 11 Maths NCERT Solutions Chapter 13 Introduction to Three Dimensional Geometry

Important Topics Class 11 Maths NCERT Solutions Chapter 13Introduction to Three Dimensional Geometry are elaborated below:

Coordinate Axes and Coordinate Planes in Three Dimensional Space

The three coordinate axes determine the three coordinate planes. The xy-plane is the plane that contains the x- and y-axes; the yz-plane contains the y- and z-axes; the xz-plane contains the x- and z-axes. These three coordinate planes divide space into eight parts, called octants.

Coordinates of a Point in Space

A cartesian plane divides the plane space into two dimensions and is useful to easily locate the points. It is also referred to as the coordinate plane. The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0).

Properties of point represented in four quadrants of coordinate planes are:

Origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).
X-axis to right of the origin O is the positive x-axis and to the left of the origin, O is the negative x-axis. The y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis.
Point represented in the first quadrant (x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis.
Point represented in the second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive y-axis.
Point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis.
Point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.

Distance between Two Points

To find the distance between two points in the coordinate plane, below-mentioned steps are followed:

Take the coordinates of two points such as (x¹, y¹) and (x², y²)
Use distance formula (i.e) square root of (x² – x¹)² + (y² – y¹)²
For this formula, calculate the horizontal and vertical distance between two points. Here, the horizontal distance (i.e) (x² – x¹) represents the points in the x-axis, and the vertical distance (i.e) (y² – y¹) represents the points in the y-axis
Square both the values such as the square of (x²– x¹) and the square of (y² – y¹)
Add both the values (i.e) (x² – x¹)² + (y² – y¹)²
Now, take the square root of the obtained value
Thus, the final value gives the distance between two points in the coordinate plane

NCERT Solutions For Class 11 Maths Chapter 12 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 12 Introduction to Three Dimensional Geometry under different exercises are as follows:

Also check:

Chapter Related Topics
Angle Between Two Plane	Angle between two lines	Angle between line and plane

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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.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

View Solution

3.
If A=\(\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}\)verify that A³-6A²+9A-4 I=0 and hence find A^-1

View Solution

4.
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

5.
Find the following integral: \(\int (ax^2+bx+c)dx\)

View Solution

6.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

View Solution

View All

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NCERT Solutions For Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry

Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry

Important Topics: Class 11 Maths NCERT Solutions Chapter 13 Introduction to Three Dimensional Geometry

NCERT Solutions For Class 11 Maths Chapter 12 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.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

3.
If A=\(\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}\)verify that A³-6A²+9A-4 I=0 and hence find A^-1

4.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

5.
Find the following integral: \(\int (ax^2+bx+c)dx\)

6.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

Similar Mathematics Concepts

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NCERT Solutions For Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry

Class 11 Maths NCERT Solutions Chapter 12 Introduction to Three Dimensional Geometry

Important Topics: Class 11 Maths NCERT Solutions Chapter 13 Introduction to Three Dimensional Geometry

NCERT Solutions For Class 11 Maths Chapter 12 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. Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

3. If A=\(\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}\)verify that A3-6A2+9A-4 I=0 and hence find A-1

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

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

6. If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that (i) \((A+B)'=A'+B' \)(ii) \((A-B)'=A'-B'\)

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.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

3.
If A=\(\begin{bmatrix}2&-1&1\\-1&2&-1\\1&-1&2\end{bmatrix}\)verify that A³-6A²+9A-4 I=0 and hence find A^-1

4.
Evaluate \(\begin{vmatrix} cos\alpha cos\beta &cos\alpha sin\beta &-sin\alpha \\ -sin\beta&cos\beta &0 \\ sin\alpha cos\beta&sin\alpha\sin\beta &cos\alpha \end{vmatrix}\)

5.
Find the following integral: \(\int (ax^2+bx+c)dx\)

6.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)