Operations in Vector Algebra

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....

Representation of Vectors

Vectors are represented by taking an arrow above the quantity, i.e. force vector is represented as  where the arrow above F represents that it is a vector quantity. Vectors can also be represented by taking their respective magnitude in x, y, and z-directions respectively. The x-direction is shown using , similarly, the y-direction is shown using  and the z-direction is shown using . Now the vector A is represented as,...

Types of Vectors

Vectors can be classified into different categories on the basis of their magnitude and direction. The various types of vectors are listed below:...

Operations in Vector Algebra

We can perform various operations in Vector Algebra by taking a geometrical approach or by taking a coordinate system approach. Various operations in vector algebra are,...

Addition of Vectors

A vector can be thought of as a displacement from point A to point B. To understand the need for the addition and subtraction of vectors, consider an example. In the figure, Laxmi goes from point A to point B and then to point C following the vectors shown in the figure. Now, after reaching point C, the net displacement made by this girl is from A to C which is given by the vector ....

Subtraction Of Vectors

Subtraction Of Vectors is similar to the addition of the vector only the director of the vector which is to be subtracted is reversed and then the addition of the vector is calculated using the vector addition formulas....

Multiplication of Vectors by Scalar

Let’s say  is a given vector and “k” be a scalar. The product of the scalar will either increase or decrease the magnitude of the vector. The direction of the vector will remain the same. The increase or decrease in the magnitude of the vector will depend upon the value of the scalar that is multiplied by the vector. The figure below shows vector A multiplied by some scalar quantity. Notice how the length of the vector changes after being multiplied by a scalar....

Multiplication of Vectors

Multiplication of two vectors is achieved in two ways...

Vector Algebra Formulas

We use various formulas in Vector Algebra to solve various types of complex problems. These formulas are very helpful in understanding and solving vector algebra problems. The important vector algebra formulas are,...

Applications of Vector Algebra

Vector algebra is widely used in various fields such as Mathematics, Engineering, Physics, and others. Various physical quantities encountered by us in real life such as force, acceleration, velocity, and others are vector quantities and we use vector algebra to define and operate on those quantities. Some of the important applications of vector algebra are...

Vector Algebra Examples

Example 1: Find the dot product of vectors P(a, b, c) and Q(p, q, r)....

FAQs on Vector Algebra

Q1: What is Vector Algebra?...