

Introduction and definitions of vector algebra
Vectors Zero definitions vectors Unit vectors A quantity that has magnitude as well as direction 


Definitoon of vector quantities, Example of vector quantities 


coinitial vectors definition 


Collinear Vectors : Two or more vectors are said to be collinear 


Equal Vectors Two vectors a and b are said to be equal, 


Graphical representation of vectors 


correction in graphical representation 


Exercise 10.1
1. Represent graphically a displacement of 40 km, 30° east of north.
2. Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 meters northwest (iii) 40°
(iv) 40 watt (v) 10
–19
coulomb (vi) 20 m/s
3. Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force
(iv) velocity (v) work done
4. In Fig 10.6 (a square), identify the following vectors.
(i) Coinitial (ii) Equal
(iii) Collinear but not equal
5. Answer the following as true or false.(i)
a and a
are 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.



Formulas and definitions for Exercise 10.2
triangle law of vector addition 


parallelogram law of vector addition 


components of a vector 


equation of vector joining two points 


section formula of vectors 


How to claculate unit vector 


How to determine direction ratio of a vector 


what is direction cosine of the vector
Exercise 10.2 Questions

13 

Compute the magnitude of vectors a = i + j + k , two different vector having same magnitide 
4 

Find the values of x and y so that the vectors 2i + 3j and xi + yj are equal 
6 

Find the sum of the vectors and unit vector in the direction of the vector 
8 

Find the unit vector in the direction of PQ vector where P and Q are the points 1, 2, 3 and 4, 5, 6, 
9 

For given vectors, a = 2i – j + 2k and b = i + j – k, find the unit vector in the direction of the 
10 

Find a vector in the direction of vector 5i – j + 2k which has magnitude 8 units 
11 

Show that the vectors 2i – 3j + 4k and – 4i + 6j – 8k are collinear 
12 

Find the direction cosines of the vector i + 2j + 3k 
13 

Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1) 
14 

Show that the vector i + j + k is equally inclined to the axes OX, OY and OZ 
15 

Find the position vector of a point R which divides the line joining two points P and Q whose posi 
17 

Show that the points A, B and C with position vectors a = 3i – 4j – 4k,b = 2i –j +k and c = i – j – 
18 

In triangle ABC which of the following is not true If a and b are two collinear vectors, then 


Definitions and furmas used in Exercise 10.4
cross pruduct all formulas and definitions with explanations 
1 

cross product examples how to find cross product of two vectors 
2 

Find a unit vector perpendicular to each of the vector a –b and a+ b where a = 3i + 2j +2k and 
3 

ncert solution for class 12 vector algebra q 3 remaining part 
4 

ncert solutions for 11 maths chapter 10 vector algebra Exercise 10.4 Question 4 and 5 
6 

Given that a b=0 and a × b = 0 What can you conclude about the vectors a and b 
8 

Show that a×(b + c) = a×b + a×c. Ncert solution for class 12 math
Misscellaneous Exercise Chapter 10

3 

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops Dete 
4 

If a+ b + c = 0, then is it true that a=b+c Justify your answer 
5 

Find the value of x for which x(i + j + k) is a unit vector 
6 

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a = 2i 3j –k and b 
7 

If a = i + j + k , b = 2i – j + 3k and c = i – 2j + k , find a unit vector parallel to the vector 
8 

Show that the points A, B and C are collinear, and find the ratio in which B divides AC. 
9 

Find the position vector of a point R which divides the line joining two points P and Q whose position ve 
9 cont 

ncert solutions for class 12 chapter 10 vector algebra miscellaneous exercise Question 9 
11 

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are 
12 

Find a vector d which is perpendicular to both a and b and c.d = 15 
13 

ncert solutions for class 12 chapter 10 vector algebra miscellaneous exercise Question 13 
14 

ncert solution for class 12 maths chapter 10 Q 14 first part 
14 cont 

If a, b ,c are mutually perpendicular vectors of equal magnitudes, show that the vector a+ b + c is 
15 

Prove that (a+b).(ab) = a^2 + b^2, if and only if a, b are perpendicular, given a≠0, b≠0. 
1619 

Objective question of maths vector algebra class 12 ncert cbse board 
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