NCERT Solutions: Exercise - 10.2 - Vector Algebra

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NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Exercise 10.2                                                                        Page No: 440 
1. Compute the magnitude of the following vectors. 
 
Solution: 
Given, vectors are 
 
2. Write two different vectors having the same magnitude. 
Solution: 
 
3. Write two different vectors having the same direction. 
Solution: 
Two different vectors having the same directions are 
Let us 
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NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Exercise 10.2                                                                        Page No: 440 
1. Compute the magnitude of the following vectors. 
 
Solution: 
Given, vectors are 
 
2. Write two different vectors having the same magnitude. 
Solution: 
 
3. Write two different vectors having the same direction. 
Solution: 
Two different vectors having the same directions are 
Let us 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
4. Find the values of x and y so that the vectors are equal 
Solution: 
Given vectors 
will be equal only if their corresponding components are equal. 
Thus, the required values of x and y are 2 and 3, respectively. 
5. Find the scalar and vector components of the vector with the initial point (2, 1) and terminal point (–5, 7). 
Solution: 
The scalar and vector components are 
The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as 
 
Page 3


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Exercise 10.2                                                                        Page No: 440 
1. Compute the magnitude of the following vectors. 
 
Solution: 
Given, vectors are 
 
2. Write two different vectors having the same magnitude. 
Solution: 
 
3. Write two different vectors having the same direction. 
Solution: 
Two different vectors having the same directions are 
Let us 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
4. Find the values of x and y so that the vectors are equal 
Solution: 
Given vectors 
will be equal only if their corresponding components are equal. 
Thus, the required values of x and y are 2 and 3, respectively. 
5. Find the scalar and vector components of the vector with the initial point (2, 1) and terminal point (–5, 7). 
Solution: 
The scalar and vector components are 
The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Thus, the required scalar components are –7 and 6, while the vector components are 
 
6. Find the sum of the vectors. 
Solution: 
Let us find the sum of the vectors. 
 
 
7. Find the unit vector in the direction of the vector. 
Solution: 
We know that 
 
 
8. Find the unit vector in the direction of vector, where P and Q are the points 
(1, 2, 3) and (4, 5, 6), respectively. 
Solution: 
We know that, 
Page 4


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Exercise 10.2                                                                        Page No: 440 
1. Compute the magnitude of the following vectors. 
 
Solution: 
Given, vectors are 
 
2. Write two different vectors having the same magnitude. 
Solution: 
 
3. Write two different vectors having the same direction. 
Solution: 
Two different vectors having the same directions are 
Let us 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
4. Find the values of x and y so that the vectors are equal 
Solution: 
Given vectors 
will be equal only if their corresponding components are equal. 
Thus, the required values of x and y are 2 and 3, respectively. 
5. Find the scalar and vector components of the vector with the initial point (2, 1) and terminal point (–5, 7). 
Solution: 
The scalar and vector components are 
The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Thus, the required scalar components are –7 and 6, while the vector components are 
 
6. Find the sum of the vectors. 
Solution: 
Let us find the sum of the vectors. 
 
 
7. Find the unit vector in the direction of the vector. 
Solution: 
We know that 
 
 
8. Find the unit vector in the direction of vector, where P and Q are the points 
(1, 2, 3) and (4, 5, 6), respectively. 
Solution: 
We know that, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
9. For given vectors and , find the unit vector in the direction of the vector  
Solution: 
We know that, 
 
10. Find a vector in the direction of the vector which has magnitude of 8 units. 
Solution: 
Firstly, 
Page 5


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Exercise 10.2                                                                        Page No: 440 
1. Compute the magnitude of the following vectors. 
 
Solution: 
Given, vectors are 
 
2. Write two different vectors having the same magnitude. 
Solution: 
 
3. Write two different vectors having the same direction. 
Solution: 
Two different vectors having the same directions are 
Let us 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
4. Find the values of x and y so that the vectors are equal 
Solution: 
Given vectors 
will be equal only if their corresponding components are equal. 
Thus, the required values of x and y are 2 and 3, respectively. 
5. Find the scalar and vector components of the vector with the initial point (2, 1) and terminal point (–5, 7). 
Solution: 
The scalar and vector components are 
The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Thus, the required scalar components are –7 and 6, while the vector components are 
 
6. Find the sum of the vectors. 
Solution: 
Let us find the sum of the vectors. 
 
 
7. Find the unit vector in the direction of the vector. 
Solution: 
We know that 
 
 
8. Find the unit vector in the direction of vector, where P and Q are the points 
(1, 2, 3) and (4, 5, 6), respectively. 
Solution: 
We know that, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
9. For given vectors and , find the unit vector in the direction of the vector  
Solution: 
We know that, 
 
10. Find a vector in the direction of the vector which has magnitude of 8 units. 
Solution: 
Firstly, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
11. Show that the vectors are collinear. 
Solution: 
First, 
 
Therefore, we can say that the given vectors are collinear. 
12. Find the direction cosines of the vector  
Solution: