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NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Miscellaneous Exercise                                                  Page No: 458 
1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis. 
Solution: 
Let us consider, 
 
2. Find the scalar components and magnitude of the vector joining the points P (x 1, y 1, z 1) and Q (x 2, y 2, z 2). 
Solution: 
First, let us consider, 
 
3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the 
girl’s displacement from her initial point of departure. 
Solution: 
It is given that 
Let O and B be the initial and final positions of the girl, respectively. 
Then, the girl’s position can be shown as 
Page 2


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Miscellaneous Exercise                                                  Page No: 458 
1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis. 
Solution: 
Let us consider, 
 
2. Find the scalar components and magnitude of the vector joining the points P (x 1, y 1, z 1) and Q (x 2, y 2, z 2). 
Solution: 
First, let us consider, 
 
3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the 
girl’s displacement from her initial point of departure. 
Solution: 
It is given that 
Let O and B be the initial and final positions of the girl, respectively. 
Then, the girl’s position can be shown as 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
Page 3


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Miscellaneous Exercise                                                  Page No: 458 
1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis. 
Solution: 
Let us consider, 
 
2. Find the scalar components and magnitude of the vector joining the points P (x 1, y 1, z 1) and Q (x 2, y 2, z 2). 
Solution: 
First, let us consider, 
 
3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the 
girl’s displacement from her initial point of departure. 
Solution: 
It is given that 
Let O and B be the initial and final positions of the girl, respectively. 
Then, the girl’s position can be shown as 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
4. If , then, is it true that ? Justify 
your answer. 
Solution: 
It is given that, 
 
 
5. Find the value of x for which is a unit vector. 
Solution: 
We know, 
Page 4


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Miscellaneous Exercise                                                  Page No: 458 
1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis. 
Solution: 
Let us consider, 
 
2. Find the scalar components and magnitude of the vector joining the points P (x 1, y 1, z 1) and Q (x 2, y 2, z 2). 
Solution: 
First, let us consider, 
 
3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the 
girl’s displacement from her initial point of departure. 
Solution: 
It is given that 
Let O and B be the initial and final positions of the girl, respectively. 
Then, the girl’s position can be shown as 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
4. If , then, is it true that ? Justify 
your answer. 
Solution: 
It is given that, 
 
 
5. Find the value of x for which is a unit vector. 
Solution: 
We know, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
6. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors 
. 
Solution: 
Let us consider that the 
 
7. If , find a unit vector parallel to the vector . 
Solution: 
Let us consider the given vectors, 
Page 5


 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
Miscellaneous Exercise                                                  Page No: 458 
1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis. 
Solution: 
Let us consider, 
 
2. Find the scalar components and magnitude of the vector joining the points P (x 1, y 1, z 1) and Q (x 2, y 2, z 2). 
Solution: 
First, let us consider, 
 
3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the 
girl’s displacement from her initial point of departure. 
Solution: 
It is given that 
Let O and B be the initial and final positions of the girl, respectively. 
Then, the girl’s position can be shown as 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
4. If , then, is it true that ? Justify 
your answer. 
Solution: 
It is given that, 
 
 
5. Find the value of x for which is a unit vector. 
Solution: 
We know, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
6. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors 
. 
Solution: 
Let us consider that the 
 
7. If , find a unit vector parallel to the vector . 
Solution: 
Let us consider the given vectors, 
 
 
 
 
NCERT Solutions for Class 12 Maths Chapter 10 – 
Vector Algebra  
 
8. Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B 
divides AC. 
Solution: 
First, let us consider, 
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