Page 261 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

13 ALGEBRA: VECTORS
SCALAR AND VECTOR QUANTITIES
In science there are two types of quantities. A quan- tity is classified as being a scalar or vector.
A scalar is a quantity which only has magnitude (or size).
For example: speed, distance, mass, volume and time.
A vector is a quantity which has both magnitude and direction.
For example: velocity, displacement, force and ac- celeration.
Representing a vector
A bold common letter may be used to name a vector. Two capital letters can also be used to name a vector.
the diagram. A vector is represented by a straight line (line
segment). The magnitude of the vector is represented by drawing the line segment using a scale. The length of the line segment indicates the magnitude of the vector.
The direction of the vector is represented by the direction of the straight line (line segment).
An arrow head on the line segment indicates the direction of the vector.
N N-E abc
The vector described by Maria’s journey which started at point A and ended at point B can be stated as AB.
The tail of the arrow indicates the starting point, and the head of the arrow indicates the ending point.
In the diagram, the horizontal shift is x and the vertical rise is y, so the vector AB can be represented
by the column matrix (or column vector).(x
)
)
That is, the horizontal displacement is parallel to the x –axis and the vertical displacement is parallel to the y-axis. In print, a vector may be named using bold letters, so AB = AB (or AB = AB).
AB= ( x y
= (horizontal displacement) vertical displacement
Ending Point
B
A
Starting Point
x
Maria walked from point A to point B as shown in
y
255
AB = ( xy
)