Vector algebra is perhaps one of the most integral aspects of Algebra. It focuses on the vector quantities, numbers and variables. In vector algebra, the essential elements generally represent vectors. As a result, diverse algebraic operations are conducted on them for the best experience.
This article will focus on understanding what vector algebra is and the different things related to it. If you are a beginner in this chapter, this article will help you score better grades by understanding it correctly.
What Is Vector Algebra?
Vectors have both directions and magnitudes. Generally, it is denoted using an arrow that depicts the direction and length it shows the magnitude. The arrow is indicative of the arrowhead, and the tail is at the opposite end. Also, two vectors are regarded to be equal directions and magnitudes.
Vector Algebra Operations
Like any other algebra where the performance of addition, subtraction, multiplication and division are essential, vector algebra also finds them critical. However, vectors contain two distinctive terminologies when regarding multiplication. This may be a cross-product and a dot product.
Addition Of Vectors
Let us take the example of vectors A and B. So, when the tail of vector B meets A’s head, the addition can be practiced. During this time, both the direction and magnitude are not allowed to change. As a result, the vector addition goes by two different laws-
Commutative Law: P + Q = Q + P and
Associative Law: P + (Q + R) = (P + Q) + R.
Subtraction Of Vectors
In this case, the direction of the remaining vectors gets reversed. This is when the addition of both vectors is performed. So, if A and B are the respective vectors for which the subtraction needs to be carried out, you need to invert the direction of the other vector. So, now you will be required to add vectors A and -B. As a result, the direction of the vectors will be opposite from one another. However, the magnitude remains stagnant.
Multiplication Of Vectors
In vector algebra, multiplication is slightly different. So, if the scalar quality is K multiplied by A, the scalar multiplication will be kA. Also, in the case of K being positive, the direction of Vector A is likely to be the same. However, in the case of the negative value, the direction of Vector kA will be opposite to the direction of vector A.
Dot And Cross Product
- Dot Product: Also known as a scalar product, it is denoted by a dot. In this case, two coordinated vectors are multiplicated so that the outcome reaches a single number.
- Cross Product: You can indicate this by a sign (x) amidst two vectors. This one is also a binary vector operation that is defined in a three-dimensional sector.
Is Vector Algebra Easy?
Yes, vector Algebra is quite an easy, scoring and exciting subject. Initially, you might find yourself fumbling around for an easy understanding of this subject. But once you get the hang of it, there is no turning back. Also, the formulas are significant to learn. So make sure you keep practicing the formulas to ace algebra exams next time.