Republic of the Philippines
Department of Education
Region III – Central Luzon
Schools Division of City of Malolos
Marcelo H. Del Pilar National High School
Bagong Bayan, City of Malolos, Bulacan
GENERAL PHYSICS 1
S.Y. 2023-2024
LESSON 2: VECTORS
Learning Objectives: The learners...
1. Differentiate vector & scalar quantities (STEM_GP12V-Ia-8)
2. Develop appreciation of safety by being aware of the
importance of vectors
3. Perform addition of vectors (STEM_GP12V-Ia-9)
4. Rewrite a vector in component form (STEM_GP12V-Ia-10)
5. Calculate directions and magnitudes of vectors
(STEM_GP12V-Ia-11)
VECTORS
In Physics, physical quantities are always involved in explaining the existence of
physical phenomenon. Physical quantities are all around us - the distance we travel
every time work is done.
Many of the physical quantities we are familiar with can be completely specified by a
single number and the appropriate wit. For example; a classroom temperature of 31°C,
physics class period last for 2 hours. A quantity that can be specified in this manner is
called a scaler. Scalar obeys standard addition and subtraction operations.
There are other quantities, however, that required not just a number and a unit for
specification, but also a direction. Such quantities are called vectors.
In this chapter, we will consider how vectors are represented, added, subtracted and
multiplied
TWO NATURES OF PHYSICAL QUANTITITES
1. Scalar Quantities - Quantities that can be described by a single number
(including any units) giving its size. (Size is referred to as the magnitude.)
- It is a physical quantity with magnitude only. Scalar
quantities can be added/ subtracted arithmetically.
Examples:
a. temperature
20°C
b. mass
85 kg
c. distance
10 m
d. speed
5 km/hr
e. electric current
7A
2. Vector Quantities - Vector quantities deal inherently with both magnitude and
direction. They can be added or subtracted vectorially.
a. Displacement
2 km in a direction 30° North of East
b. Velocity
10 kph North
c. Force
98 N downward
d. Acceleration due to gravity 9.8 𝑚/𝑠 !
e. Momentum
10 kg • m/s toward +x-axis
Address: Bagong Bayan, City of Malolos, Bulacan
Telephone No.: (044) 795-5343
E-Mail Address: 300751@deped.gov.ph
"
f. Electric Field
g. Magnetic Field
h. Current Density
17
#
23 T from N to S
75 𝐴/𝑚! +terminal to - terminal
VECTOR REPRESENTATION
Line segment from P to Q which is 10m represents magnitude.
Arrowhead indicates the sense of direction from P to Q.
The magnitude of a vector is a nonnegative number with a unit that indicates the size
of the vector without regard to its direction. It is independent of its direction.
The length of the arrow must be divided according to the equivalent magnitude of vector
quantity and of accurate scale.
ADDITION OF VECTORS
Vector addition is commutative and associative.
1. GRAPHICAL METHOD
• A diagram is constructed in which the arrows are drawn tail to head or
head to tail except in parallelogram method wherein it uses tail to tail.
• The length of the arrows representing the vectors magnitudes are drawn
to scale.
• The angles representing directions are shown accurately using a
protractor.
• The length of the arrow representing the resultant vector is measured
using a ruler.
• The measured length of the resultant vector will be converted back into
the original nature of vectors carrying its unit using the scale factor.
a. Triangle Method
b. Parallelogram Method
2. ANALYTICAL METHOD
a. Law of Cosine
In a triangle, the square of hypotenuse side is equal to the sum of the
square of the other two sides minus twice their products times the cosine
of the included angle.
Address: Bagong Bayan, City of Malolos, Bulacan
Telephone No.: (044) 795-5343
E-Mail Address: 300751@deped.gov.ph
b. Law of Sine
In a triangle, any two sides are proportional to the sine of the opposite
angles.
c. Pythagorean Theorem
In a right triangle, the square of the hypotenuse side is equal to the sum
of the square of the other two sides
d. Trigonometric Functions
3. COMPONENT METHOD
Address: Bagong Bayan, City of Malolos, Bulacan
Telephone No.: (044) 795-5343
E-Mail Address: 300751@deped.gov.ph
SAMPLE PROBLEMS:
1. Given in the figure, four concurrent vector quantities, find the resultant using
triangle method.
2. Find by using the component method the resultant of the following three
vectors: A = 30.0 units at 30° with the x-axis, B = 20.0 units at 120° with the xaxis and C = 10.0 units at 225° with the x-axis.
Address: Bagong Bayan, City of Malolos, Bulacan
Telephone No.: (044) 795-5343
E-Mail Address: 300751@deped.gov.ph
3. A vector force A has a magnitude of 150 N and is oriented 25.0° clockwise from
the vertical. Vector force B has a magnitude of 110 N and points 40.0° below
the horizontal. Find the magnitude and direction of the resultant force vector C
by means of component method.
4. A car travels 9.00 km East and then 6.00 km, 30.0° North of East. Find the
displacement of the car by applying the law of cosines and the law of sine.
5. Two cars are moving on an open surface. One has the velocity components 𝑉$% =
2.0 m/s, 𝑉&% = 3.0 m/s. The other has the velocity components 𝑉$! = 3.0 m/s,
𝑉&! = 4.0 m/s. If both cars started from the same point, determine the angle
between them.
6. Two tugboats are towing as barge. Each exerts a force of 5.0 tons, and the angle
between two ropes is 30°. Find the resultant force exerted on the barge.
References:
1. Physics I (Engr. Sergio D. Buhain et. al.)
2. University Physics (Young and Freedman)
3. Engineering Mechanics (Ferdinand Singer)
ENGR. ROWELL A. DEMDAM
Address: Bagong Bayan, City of Malolos, Bulacan
Telephone No.: (044) 795-5343
E-Mail Address: 300751@deped.gov.ph