CH 05
X-PHYSICS
VECTORS
FAHAD AKHTER
SCALAR QUANTITIES (SCALARS):
“All those quantities which are completely specified by only their unit and magnitude is called scalar
quantities E.g. Length, mass, time etc.”
VECTOR QUANTITIES (VECTORS):
“All those quantities which are not completely specified by only their unit and magnitude as well as
direction is required is called vector quantities” E.g. Momentum, Velocity, Acceleration etc.
⃗ , ⃗⃗⃗
Vector are representing by arrow on the head of the quantities. E.g.𝐏
𝐕, ⃗⃗⃗⃗
𝐚 𝐞𝐭𝐜
NEGATIVE OF A VECTOR:
“If two vectors having same magnitude but opposite in direction, then the vectors are called negative
of each other.”
A
-A
RESULTANT VECTOR:
“Resultant vector is the sum of two or more vector which gives the combine effect of all vectors to be
added.”
RESOLUTION OF VECTOR:
“The process of splitting of vectors into its components is called resolution of vector.”
ADDITION OF VECTOR BY HEAD TO TAIL RULE:
When two or more than two vectors are added then
the head of the first is joined with the tail of the
second vecotr and head of the first is joined with the
tail of the third vector and so on. In this way all the
vectors to be added are joined together. The
resultant is obtain the joining the tail of the first vector
with the head of the last vwctor by a straight line. The
length of thus line represents the magnitude of the
resultant.

RESOLUTION OF VECTOR:
“The process of a splitting up a single vector into two or more vector is called resolution of
vectors.”

COMPONENTS:
The vectors whose vector sum is equal to a given vector are called component of that vector.

HORIZONTAL COMPONENTS:
The component of a vector Fx which is directed along x-axis is known as horizontal
component.
Fx = F COS θ

VERTICAL COMPONENTS:
The component of a vector Fy which is directed along y-axis is known as vertical component.
Fy = F SIN θ

COMPOSITION OF VECTOR BY RECTANGULAR COMPONENT METHOD:
If the rectangular components of a vector are given, the magnitude and direction of the vector
Can be obtain thus a vector can be specified by its two rectangular components.
X-PHYSICS

FAHAD AKHTER
FORMULA FOR MAGNITUDE:

Consider rectangular component Fx and Fy which are represented by directed line
segments OA and OB respectively, both magnitude and direction.

Adding these two components by head to tail rule it can be seen that the directed line
segments OC represents, in both magnitude and direction of F.

To drive the expression for the magnitude and direction of F in terms of magnitude of Fx
and Fy consider the right angle triangle OAC.
By using Pythagoras theorem we have
|Hyp|2 = |Base|2 + |Perp|2
|OC|2 = |OA|2 + |AC|2
|F|2 = |F COS θ|2 + |F SIN θ|2
|F|2 = |Fx|2 + |Fy|2
𝐅 = √𝐅𝐱 𝟐 + 𝐅𝐲 𝟐
The above formula gives us magnitude of the resultant vector F.

FORMULA FOR DIRECTION:
The direction of F is determined by finding the angle θ which the vector F makes with x-axis. In
the right angle triangle OAC, we have.
𝐅 𝐒𝐈𝐍 𝛉
𝐭𝐚𝐧𝛉 =
𝐅 𝐂𝐎𝐒 𝛉
𝐀𝐂
𝐭𝐚𝐧𝛉 =
𝐎𝐂
𝐅𝐲
𝐭𝐚𝐧𝛉 =
𝐅𝐱
𝐅𝐲
𝛉 = 𝐭𝐚𝐧−𝟏
𝐅𝐱
The above formula gives us direction of the resultant vector F.
*This is extra section just for knowledge.
KEY TO REMEMBER:



Trigonometric ratio was first introduced by the Muslim mathematician Muhammad Bin Musa
Khwarizmi.
The magnitude of resultant of two or more vectors which are the same direction is equal to the
sum of their magnitudes its directions remain the same.
Vectors in three-dimensional space (1978) is a book concerned with physical quantities
defined in "ordinary" 3-space. It was written by J.S.R. Chisholm, an English mathematical
physicist, and published by Cambridge University Press.
CH 05
MULTIPLE CHICE QUESTIONS (Mcq’S)
1. The process of splitting up vectors into its components is called
.
i) Addition of vector
ii) Composition of vector
iii) Resolution of vector
2.
Is scalar quantity.
i) Displacement
ii) Force
iii) Weight
3.
i) Mass
iii) Displacement
4.
Is vector quantity.
ii) Weight
The x-component of force ‘F’ acting at an angle ‘θ’ with the axis is given by the formula
.
i) FCosθ
ii) FSinθ
iii) Ftanθ
X-PHYSICS
FAHAD AKHTER
5. The angle between rectangular component of a vector is
i) 900
ii) 600
iii) 450
6. Vector is added graphically by using
.
i) Right hand rule
ii) Head to tail rule
7. A scalar has no
i) Number
.
iii) Left hand rule
.
ii) Unit
8. Displacement is an example of
i) Scalar
ii) Vector
iii) Direction
.
9.
Those physical quantities which are completely expressed by numbers a suitable unit as well as
direction are called
quantities.
i) Scalar
ii) Vector
10. Those physical quantities which are completely expressed by numbers a suitable unit are called
quantities.
i) Scalar
ii) Vector
CH 05
PAST TEN YEARS QUESTIONS
 2003
Q: An aero plane is flying at a velocity of 600 Km/h dives make an angle of 300 with the velocity
direction. Find the velocity of its shadow on the ground, if the sun is vertically above the plane.
(Take sin 1300 = 0.5)
Q: Torque Vector is quantity?
 2004
Q: Define negative of a vector?
Q: The angle b/w the rectangular component of a vector is 900.
Q: A force of 100w acts at an angle of 300 with the horizontal find its horizontal and vertical
components when sin 300=0.5 and co3 300=0.866?
 2005
Q: Define scalar and vector quantities and give two example of each?
 2006
Q: Define scalars?
Q: Define resultant vector and describe the addition of vector by head to tail rule?
 2007
Q: Define addition of vector?
Q: A roller tied to a string is dragged on a floor making an angle of 600 with the floor. If the tension in
the string is 20N. Fine the force by which roller is dragged (Cos 600 = 0.5 & Sin 600 = 0.866)
 2008
Q: Write two points of difference between each of the following I) Scalar and vector.
 2009
Q: Define resolution of vector? How is a vector resolve into its component vector?
 2010
Q: If Fx and Fy are the horizontal and vertical component of vector F. Write down the formula for the
magnitude of F. Show Fx, Fy, & F by diagram.
X-PHYSICS
FAHAD AKHTER
 2011
Q: Define resolution of vector & write down two formulae of rectangular components?
 2012
Q: With the help of trigonometric ratios, find the magnitude of horizontal and vertical component of
vector?
Q: A force of 100N act at an angle of 600 with the horizontal. Find its horizontal and vertical
components, where cos600 = 0.5 and Sin600 = 0.866
A man is an architect of his own future.