Name: _________________
Grade Level: 12
Strand: STEM
Teacher: Eugene M. Bordey
Quarter/Domain
1
ST
Quarter General
Physics 1
Week & Day No.
Week 8/
September 20, 2024
Lc Code
STEM _GP12EU-Ia-1-
3,5,8,9
LEARNING ACTIVITY SHEET
Write your answers on a short bond paper.
TOPIC: Vectors
Learning Competency: Solve measurement problems
I. OBJECTIVES: Convert of units, express measurements in scientific notation; Differentiate accuracy from precision;
Differentiate random errors from systematic errors; Estimate errors from multiple measurements of a physical quantity using
variance; Differentiate vector and scalar quantities; Perform addition of vectors
II. LESSON OVERVIEW
What is VECTOR QUANTITY?
VECTORS are quantities that have both magnitude and direction. There are numerous ways of representing a vector which
include
๎
โ, F (boldface), and
๎
โ=๎๎
.๎
๎
๎
@๎๎๎๎ ๎๎ ๎๎
ยฐ
๎
A Cartesian coordinate system (named after Rene Descartes 17
th
C, allowing expression of problems in geometry in terms
of algebra and calculus) in two dimensions is defined by an ordered pair or perpendicular lines (axes).
A point in space in a Cartesian coordinate system may also be represented by a position vector, which can be thought of as
an arrow pointing from the origin of the coordinate system to the point. If the coordinates represent spatial positions
(displacements), it is common to represent the vector from the origin to the point of interest as r. In two dimensions, the
vector from the origin to the point with Cartesian coordinates x,y can be written as ๎=๎๎,+๎๎, where ๎=
๎
๎
and ๎=
๎
๎
. The
normalized vector of a non zero-vector is the unit vector for the direction. Unit vector may be used to represent the axes of a
Cartesian coordinate system.๎=๎1
0
0๎ ๎=๎0
1
0๎ ๎ก=๎0
0
1๎ . Therefore ๎=๎ข1
0๎ฃ and ๎=๎ข0
1๎ฃ
The point where the axes meet is taken as the origin of both, thus turning each axis into a number line. In common usage,
the abscissa refers to the x coordinate and the ordinate refers to the y coordinate of a standard two-dimensional graph.
The two axes divide the place into four right angle called quadrants. A cartesian coordinate system for a three dimensional
space consists of an ordered triplet of lines that go through a common point (the origin). Each pair of axes defines coordinate
system. Standard names for the coordinates in the three axes are abscissa, ordinate, and applicate, denoted by the letters
(๎,๎,๎ก). These planes divide space into eight octants. The octants are (+๎,+๎,+๎ก), (+๎,โ๎,โ๎ก), (โ๎,+๎,+๎ก), (โ๎,+๎,โ๎ก),
(+๎,โ๎,+๎ก), (โ๎,โ๎,+๎ก), (+๎,+๎,โ๎ก), (โ๎,โ๎,โ๎ก).
A point in space in a cartesian coordinate system may also be represented by a position vector, which can be thought of as
an arrow pointing from the origin pointing from the origin of the coordinate system to the point.
Examples of VECTORS are: Force, Velocity, Acceleration, Displacement
Vector D points ๎๎
ยฐ
North of East
Vector A points North
Vector B points ๎ง๎
ยฐ
North of West
Vector C points ๎๎
ยฐ
East of South
EQUAL VECTORS
Vectors are equal when they have the same magnitude and direction.
NEGATIVE VECTORS
The vector (-) A has the same magnitude as the vector (+) A but has opposite direction.
TWO TYPES OF VECTORS
Free Vectors โ Vectors that can be described by expressing their magnitude and direction.
Localized Vectors - Vectors that cannot be described completely by just specifying its magnitude and direction, but also by
specifying the line along which its representative segment lies. The tails of such vectors are always fixed.
VECTOR APPLICATIONS
Navigation, Engineering, Science, Economics, etc.
For example, velocity is a vector because it describes both how fast something is moving
and in what direction it is moving.
How to perform addition of vectors?
In order to add two vectors, we think of them as displacements. Displacements is simply a change in position of a point.
