Properties of Vectors
Vectors are mathematical objects and we will now study some of their mathematical properties. If two vectors have the same magnitude (size) and the same direction, then we call them equal to each other. Two vectors are equal if they have the same magnitude ...
Properties of Vectors
Vectors are mathematical objects and we will now study some of their mathematical properties.
If two vectors have the same magnitude (size) and the same direction, then we call them equal to each other. For example, if we have two forces, \(\vec{F_{1}} = \text{20}\text{ N}\) in the upward direction and \(\vec{F_{2}} = \text{20}\text{ N}\) in the upward direction, then we can say that \(\vec{F_{1}} = \vec{F_{2}}\).
Definition: Equality of Vectors
Two vectors are equal if they have the same magnitude and the same direction.
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 direction opposite to the reference positive direction. For example, if in a particular situation, we define the upward direction as the reference positive direction, then a force \(\vec{F_{1}} = \text{30}\text{ N}\) downwards would be a negative vector and could also be written as \(\vec{F_{1}} = -\text{30}\text{ N}\). In this case, the negative sign (\(-\)) indicates that the direction of \(\vec{F_{1}}\) is opposite to that of the reference positive direction.
Definition: Negative Vector
A negative vector is a vector that has the opposite direction to the reference positive direction.
Like scalars, vectors can also be added and subtracted. We will investigate how to do this next.
This lesson is part of:
Vectors and Scalars