NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 10

Vector Algebra Class 12

Chapter 10 Vector Algebra Exercise 10.1, 10.2, 10.3, 10.4, miscellaneous, miscellaneousmiscellaneous Solutions

<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise 10.1 : Solutions of Questions on Page Number : 428

Q1 :  

Represent graphically a displacement of 40 km, 30° east of north.


Answer :

Here, vector represents the displacement of 40 km, 30° East of North.

Answer needs Correction? Click Here

Q2 :  

Classify the following measures as scalars and vectors.

(i) 10 kg (ii) 2 metres north-west (iii) 40°

(iv) 40 watt (v) 10-19 coulomb (vi) 20 m/s2


Answer :

(i) 10 kg is a scalar quantity because it involves only magnitude.

(ii) 2 meters north-west is a vector quantity as it involves both magnitude and direction.

(iii) 40° is a scalar quantity as it involves only magnitude.

(iv) 40 watts is a scalar quantity as it involves only magnitude.

(v) 10-19 coulomb is a scalar quantity as it involves only magnitude.

(vi) 20 m/s2 is a vector quantity as it involves magnitude as well as direction.

Answer needs Correction? Click Here

Q3 :  

Classify the following as scalar and vector quantities.

(i) time period (ii) distance (iii) force

(iv) velocity (v) work done


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

In Figure, identify the following vectors.

(i) Coinitial (ii) Equal (iii) Collinear but not equal


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Answer the following as true or false.

(i) andare collinear.

(ii) Two collinear vectors are always equal in magnitude.

(iii) Two vectors having same magnitude are collinear.

(iv) Two collinear vectors having the same magnitude are equal.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise 10.2 : Solutions of Questions on Page Number : 440

Q1 :  

Compute the magnitude of the following vectors:


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Write two different vectors having same magnitude.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Write two different vectors having same direction.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the values of x and y so that the vectors are equal


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (-5, 7).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find the sum of the vectors.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Find the unit vector in the direction of the vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the unit vector in the direction of vector, where P and Q are the points

(1, 2, 3) and (4, 5, 6), respectively.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the unit vector in the direction of vector, where P and Q are the points

(1, 2, 3) and (4, 5, 6), respectively.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find a vector in the direction of vector which has magnitude 8 units.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Show that the vectorsare collinear.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Find the direction cosines of the vector


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Find the direction cosines of the vector joining the points A (1, 2, -3) and

B (-1, -2, 1) directed from A to B.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Show that the vector is equally inclined to the axes OX, OY, and OZ.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ration 2:1

(i) internally

(ii) externally


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, - 2).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Show that the points A, B and C with position vectors,, respectively form the vertices of a right angled triangle.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

In triangle ABC which of the following is not true:

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

If are two collinear vectors, then which of the following are incorrect:

A. , for some scalar λ

B.

C. the respective components of are proportional

D. both the vectors have same direction, but different magnitudes


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise 10.3 : Solutions of Questions on Page Number : 447

Q1 :  

Find the angle between two vectorsandwith magnitudesand 2, respectively having.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the angle between the vectors


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Find the projection of the vectoron the vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the projection of the vectoron the vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Show that each of the given three vectors is a unit vector:

Also, show that they are mutually perpendicular to each other.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Findand, if.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Evaluate the product.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Find the magnitude of two vectors, having the same magnitude and such that the angle between them is 60° and their scalar product is.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find, if for a unit vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Ifare such thatis perpendicular to, then find the value of λ.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Show that is perpendicular to, for any two nonzero vectors


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

If, then what can be concluded about the vector?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

If are unit vectors such that , find the value of .


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

If either vector, then. But the converse need not be true. Justify your answer with an example.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectorsand]


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, -1) are collinear.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Show that the vectorsform the vertices of a right angled triangle.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

Ifis a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λis unit vector if

(A) λ = 1 (B) λ = –1 (C)

(D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise 10.4 : Solutions of Questions on Page Number : 454

Q1 :  

Find, if and.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find a unit vector perpendicular to each of the vector and, where and.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

If a unit vector makes an angleswith with and an acute angle θ with, then find θ and hence, the compounds of.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Show that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find λ and μ if .


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Given that and. What can you conclude about the vectors?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Let the vectors given as . Then show that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

If either or, then. Is the converse true? Justify your answer with an example.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and

C (1, 5, 5).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find the area of the parallelogram whose adjacent sides are determined by the vector .


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Let the vectors and be such that and, then is a unit vector, if the angle between and is

(A) (B) (C) (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Area of a rectangle having vertices A, B, C, and D with position vectors and respectively is

(A) (B) 1

(C) 2 (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 458

Q1 :  

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Find the scalar components and magnitude of the vector joining the points

.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

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.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

If, then is it true that? Justify your answer.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the value of x for whichis a unit vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

If, find a unit vector parallel to the vector.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

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.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors areexternally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Let and. Find a vector which is perpendicular to both and, and.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

The scalar product of the vectorwith a unit vector along the sum of vectors and is equal to one. Find the value of.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Prove that, if and only if are perpendicular, given.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

If θ is the angle between two vectors and , then only when

(A) (B)

(C) (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Let and be two unit vectors andθ is the angle between them. Then is a unit vector if

(A) (B) (C) (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

The value of is

(A) 0 (B) –1 (C) 1 (D) 3


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

If θ is the angle between any two vectors and, then when θisequal to

(A) 0 (B) (C) (D) π


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Exercise Miscellaneousmiscellaneous : Solutions of Questions on Page Number : 458

Q1 :  

The two adjacent sides of a parallelogram areand .

Find the unit vector parallel to its diagonal. Also, find its area.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 9 : Differential Equations Next Chapter 11 : Three Dimensional Geometry >>

Maths Part-2 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Vector Algebra ( Exercise 10.1, 10.2, 10.3, 10.4, miscellaneous, miscellaneousmiscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles