CHAPTER 20. VECTORS AND SCALARS 20.2
Properties of vectors ESAGN
Vectors are mathematical objects and we will now study some of their mathematical prop-
erties.
If two vectors have the same magnitude (size)andthe same direction, then we call them
equal to each other. For example, if we have two forces,
→
F 1 = 20Nin the upward direction
and
→
F 2 = 20Nin the upward direction, then we can say that
→
F 1 =
→
F 2.
DEFINITION: Equality of vectors
Two vectors are equal if they have thesamemagnitude and thesamedirec-
tion.
Just like scalars which can have positive or negative values, vectors can also be positive
or negative. A negative vector is a vector which points in the directionoppositeto the
reference positive direction. For example, if in a particular situation, we define the upward
direction as the reference positive direction, then a force
→
F 1 = 30Ndownwardswould be a
negative vectorand could also be written as
→
F 1 =− 30 N. In this case, the negative (-) sign
indicates that the direction of
→
F 1 is opposite to that of the reference positive direction.
DEFINITION: Negative vector
A negative vector is a vector that has theoppositedirection to the reference
positive direction.
Like scalars, vectors can also be added and subtracted. We will investigate how to do this
next.
Physics: Mechanics 371