What Is Vector Algebra?
Vector algebra is the type of Algebra that is used to perform various algebraic operations on vectors. As we know vectors are quantities that have both magnitude and direction whereas scalar quantities only have magnitude and no direction. The difference between vector quantities and scaler quantities can be understood with the help of the example discussed below.
The height and weight of a person can be described by a single number like 75 Kg or 150cm. These quantities only have magnitude, they do not require any extra information. Such quantities are called scalar quantities.
Now, let’s consider another situation, the coach of the football team wants to teach his goalkeeper to pass the ball to another player, now he will have to describe the region he should send the ball (Direction) and how hard he should hit (magnitude). This quantity requires both magnitude and direction. Such quantities are called vectors.
Such quantities in which direction are present are called Vector quantities. Examples of vector quantities are Displacement, Velocity, Force, etc. As these quantities have directions operations on these quantities are not easily applied and the concept of vector algebra is used to perform operations on these quantities.
In the above figure, the length of the line shows the magnitude of the vector, and the arrowhead points to its direction. It is basically a directed line segment . Its starting point A is called the initial point and point B where it ends is called the terminal point.
Vector Algebra
Vectors algebra is the branch of algebra that involves operations on vectors. Vectors are quantities that have both magnitude and direction so normal operations are not performed on the vectors. We can add, subtract, and multiply vector quantities using special vector algebra rules. Vectors can be easily represented in 2-D or 3-D spaces. Vector algebra has various applications it is used in solving various problems in mathematics and physics, engineering, and various other fields.
In this article, we will learn about vector algebra, operations in vector algebra, types of vectors, and others in detail.