Operation in Vector
The different operations performed with vector quantities are tabulated below with their notation and illustration.
| Operation | Notation | Illustration |
|---|---|---|
Vector Addition | r1 + r2 | Addition of two vectors gives a vector |
Scalar Multiplication | q.r1 | Multiplying a vector ‘r1‘ with scalar ‘q’ result in a vector |
Dot Product | r1 · r2 | Dot product of two vectors gives a scalar |
Cross Product | r1 ⨯ r2 | Cross product of two vectors gives a vector |
Scalar Triple Product | r1 · (r2 ⨯ r3) | Dot Product of Cross product of two vectors |
Vector Triple Product | r1 ⨯ (r2 ⨯ r3) | Cross Product of Cross Product of two Vectors |
Learn More, Dot and Cross Product of Vectors
Vector Calculus in Maths
Vector Calculus in maths is a sub-division of Calculus that deals with the differentiation and integration of Vector Functions. We already know that Calculus is a branch of mathematics that deals with the rate of change of a function concerning another function. There are two major divisions of Calculus namely, Differential Calculus and Integral Calculus.
The branch of Differential Calculus deals with the process of finding derivatives or differentiation of functions while Integral Calculus deals with finding the antiderivative of a function whose derivative is given. In this article, we will learn in detail about Vector Calculus which is a lesser-known branch of calculus, and the basic formulas of Vector Calculus.
In this article, you are going to read everything about what is vector calculus in engineering mathematics, vector calculus formulas, vector analysis, etc.
Table of Content
- What is Vector Calculus?
- Operation in Vector
- Divergence and Curl
- Vector Calculus Formulas
- Vector Calculus Identities
- Vector Calculus Applications
- Solved Examples
- FAQs
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