Physics Chapter 2 – Vectors and Equilibrium (Class 11) for FSC, Entry Tests & NTS Preparation
Chapter 2, Vectors and Equilibrium, is an important topic for Class 11 students preparing for FSC board exams, engineering entry tests like ECAT, NUST, FAST, and NTS exams. This chapter explains the concepts of vectors, vector operations, and the conditions required for a body to be in equilibrium. Understanding vectors and equilibrium is essential for solving problems in mechanics and applied physics.
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Consider a car is travelling for one hour. In which of the following cases is the average velocity zero?
PMC Practice 2
Physics
Scalars and Vectors
Elimination Tool:
Instantaneous velocity is:
PMC Practice 1
Physics
Scalars and Vectors
Elimination Tool:
If the dot product of vectors Is equal to product of their magnitudes, the angle between them
Consider a car is travelling for one hour. Which of the following trips have the same average velocity?
PMC Practice 2
Physics
Scalars and Vectors
Elimination Tool:
Vector components In space are
If y-component of a force acting In y direction is 6N the x-component will be
A vector such as the velocity of a body undergoing uniform translational motion, which can be displaced parallel to itself and applied to any point is known as:
NTS 2010
Physics
Scalars and Vectors
Elimination Tool:
If the unit vectors i, j, k are perpendicular to each other therefore
i.i = j.j = k.k = ______.
I.j = j.k = k.i = ______.
NTS 2016 SMBBMC
Physics
Scalars and Vectors
Elimination Tool:
A body will be in translational equilibrium if the vector sum of all the forces acting on it is:
NUMS 2017
Physics
Scalars and Vectors
Elimination Tool:
Velocity is a:
PMC Practice 3
Physics
Scalars and Vectors
Elimination Tool:
Which unit is used in the measurement of Displacement?
PMC Practice 4
Physics
Scalars and Vectors
Elimination Tool:
The scalar product of (2i – j + 3k) . (31 + 2j – k) i?
NTS 2014
Physics
Scalars and Vectors
Elimination Tool:
i.(j*k)
A vector having magnitude equal to one is called
What is the projection of E = 2i-3j+6k onto the direction of vector F=i+2j+2k.
NTS 2016 DUHS & JSMU
Physics
Scalars and Vectors
Elimination Tool:
If the magnitude of vectors A, B and C is 12, 5 and 13 units respectively and A + 13 = What will be the angle between vectors A and B?
How much angle does the vector 2i+3j makes with y axis.
What happens to bulk of potential energy of a glass that falls from a table and breaks
Dimension of Torque Is?
The displacement has __________.
PMC Practice 2
Physics
Scalars and Vectors
Elimination Tool:
Displacement is a:
PMC Practice 2
Physics
Scalars and Vectors
Elimination Tool:
If x-component of a vector is v3 and y-component is 1, then the angle made by the vectoralong x-axis is:
ETEA 2017
Physics
Scalars and Vectors
Elimination Tool:
The cross product of three unit vectors (i, j, k) equals
What is the angle made by the vector -i-5j with x-axis?
Find the work done in moving an object along a straight line from (3,2,−1) to (2,−1,4) in a force field given by F=4i^−3j^+2k^.
NTS 2013
Physics
Scalars and Vectors
Elimination Tool:
Which pair includes a vector quantity and a scalar quantity respectively?
NTS 2017
Physics
Scalars and Vectors
Elimination Tool:
If ‘0.8 i + 0.5 j + ck’ represents a unit vector, the value of ‘c’ is:
NUMS 2019 Cancelled
Physics
Scalars and Vectors
Elimination Tool:
Displacement of sun with respect to earth is
PMC Sample 2
Physics
Scalars and Vectors
Elimination Tool:
If the velocity v being a vector quantity is multiplied to scaler quantity mass, the result will be:
R1 and R2 are two-position vectors making angles θ1 and θ2 with positive X-axis respectively. Their vector product is:
[R1 = 4 cm, R2 = 3 cm , e1 = 30 degrees , e2 = 90 ]
NTS 2011
Physics
Scalars and Vectors
Elimination Tool:
Rain is vertically downwards with the velocity of 30m/s , a wind blows from north to south direction with 10m/s then at what angle should the umbrella of the person be held and in which
All of the following is/are scalar quantities except:
NTS 2011
Physics
Scalars and Vectors
Elimination Tool:
Evaluate the scalar product of the following: k.( i + j) ?
NTS 2015 SMBBMC
Physics
Scalars and Vectors
Elimination Tool:
If a rotating body is moving anti-clockwise, the direction of angular velocity is:
PMC Practice 1
Physics
Scalars and Vectors
Elimination Tool:
Which of the following option(s) represent a vector quantity?
The resultant of two forces has magnitude of 20N . if one of the forces is of magnitude 20√3 N and makes an angle of 30o with the resultant then, the other forces must be of magnitude:
NTS 2015 DUHS and JSMU
Physics
Scalars and Vectors
Elimination Tool:
If a force of 2N acting through a moment arm of V2 rn produces a torque of V6 Nm, what is the angle between F and r.
Vector is quantity that ——
PMC Practice 4
Physics
Scalars and Vectors
Elimination Tool:
Two vectors A and B both have magnitude of 5N and the angle between them is 135, then magnitude of A x B will be
Work is a
PMC Sample 2
Physics
Scalars and Vectors
Elimination Tool:
Two vectors are of magnitude 50 and 31,the resultant might be?
(1, 1, 1) • (2, 2, 2) =
Two vectors S and R are such that S= 4, R= 6 and S.R= 13.5. Find the angle between S and R.
NTS 2015 SMBBMC
Physics
Scalars and Vectors
Elimination Tool:
The acceleration is a _____.
PMC Practice 6
Physics
Scalars and Vectors
Elimination Tool:
The scalar or Dot product of Vectors (3i – 2j + 4k) and (2i + 2j – 3k) is _____.
NTS 2019
Physics
Scalars and Vectors
Elimination Tool:
Three books A, 8, C are place on each other with A on top, B in mid and C at bottom. If weight of A is 2N, B is 5N and that of C is 4N, what is the total force being exerted on book B?
Which quantity is a scalar quantity
PMC Sample 3
Physics
Scalars and Vectors
Elimination Tool:
{j * j}.i
A vector in space has _____ dimension:
NUMS 2017
Physics
Scalars and Vectors
Elimination Tool:
If A and B arc two vectors, area of parallelogram formed by these vectors will be?
- a) AB b) A . c) AB cos 0 d) lAx131
Two vectors of magnitude 10m and 20m have an angle 30° between them. The component of shorter vector parallel to the longer vector will be:
A particle moves from position r = 3i+2j-6k to r = 14i+13j+9k under the action of a Force F = 8i+2j+6k. Find the work done
by the force:
NTS 2010
Physics
Scalars and Vectors
Elimination Tool:
The vector product of two vectors A and B is ____ vectors A and B.
NTS 2019
Physics
Scalars and Vectors
Elimination Tool:
If A = B + C and A, B, C have scalar magnitudes of 5, 4, 3 units respectively then the angle between vector A and Vector C is:
NUMS 2014
Physics
Scalars and Vectors
Elimination Tool:
If a Force F of magnitude 5N makes an angle of 60 with x-axis, the x-component of the vector will
be:
A constant force F= 2i + 3j +4k is applied on a body. What will be the work done to move the body 5m in the z-direction?
PMC Sample 1
Physics
Scalars and Vectors
Elimination Tool:
Key Concepts about Vectors and Equilibrium
The chapter explains vectors, scalars, and their representation in physics. It covers vector addition and subtraction using graphical and analytical methods, resolution of vectors, and components of a vector. The chapter also discusses equilibrium of a particle and a rigid body, including conditions for translational and rotational equilibrium. Each concept is explained with examples, diagrams, and practical applications. These concepts are highly important for FSC board exams, engineering entry tests like ECAT, NUST, FAST, and NTS exams.
Free Entry Test & NTS Preparation
Mastery of vectors and equilibrium helps students understand forces, solve mechanics problems, and analyze physical systems. PLS Academy provides practice questions, solved past papers, and chapter-wise MCQs to help students revise these topics effectively. Regular study of this chapter improves problem-solving skills, conceptual clarity, and exam performance, ensuring students are well-prepared for FSC board exams, competitive entry tests, and NTS exams.
JazakAllah.
