NCERT Solutions Miscellaneous Exercise: Vector Algebra

# NCERT Solutions Miscellaneous Exercise: Vector Algebra | Mathematics (Maths) for JEE Main & Advanced PDF Download

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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
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
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
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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## Mathematics (Maths) for JEE Main & Advanced

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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