Vector-Calculus Archives

Orthogonal Vectors: Definition, Formula and Examples

Last Updated: 08 August 2024

Orthogonal vectors are a fundamental concept in linear algebra and geometry. Orthogonal vectors are vectors that are perpendicular to each other, meaning they meet at a ri...read more

Vector Triple Product Practice Problems

Last Updated: 18 June 2024

Vector triple product involves three vectors. When you take the cross product of the vectors B and C, and then take the cross product of the result with vector A, it gives...read more

Fourier Trigonometric Series : Definition , Formula and Practice Questions

Last Updated: 01 August 2024

Fourier trigonometric series is a way to represent a periodic function as a sum of sine and cosine functions. This series was named after the French mathematician Joseph F...read more

Conservative Vector Fields

Last Updated: 25 July 2024

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integra...read more

Last Updated: 30 July 2024

Negative Vector or Negative of a Vector is vector with same magnitude but in opposite direction. The negative of a vector is obtained by multiplying the vector by -1. This...read more

Divergence Theorem Practice Problems

Last Updated: 21 August 2024

The Divergence Theorem is a fundamental result in vector calculus and physics. It relates the flux of the vector field through a closed surface to the divergence of the fi...read more

Engineering Mathematics

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Vector-Calculus

Practice Questions

Modulus and Conjugate of a Complex Number

Last Updated: 19 September 2024

Complex numbers find application in different areas of mathematics and engineering science. With complex numbers, there are two significant values: modulus and conjugate. ...read more

How to find the slope for a three-dimensional line?

Last Updated: 05 November 2024

In three dimensions, lines don’t have a single slope like in 2D. Instead, use the direction vector, which shows the line’s direction. To find it:Identify two points on the...read more

Basis and Dimension in Vector Space

Last Updated: 06 December 2024

Vector Spaces are a fundamental concept in machine learning and mathematics, providing the structure for various operations in high-dimensional data processing. A vector s...read more

Last Updated: 02 July 2025

A vector norm, sometimes represented with a double bar as ∥x∥, is a function that assigns a non-negative length or size to a vector x in n-dimensional space. Norms are ess...read more

Last Updated: 27 January 2025

In mathematics, vectors are fundamental objects that represent quantities with both magnitude and direction. They are widely used in various branches of mathematics, phys...read more

Vector Algebra Practice Questions (Easy)

Last Updated: 20 January 2025

Vector Algebra is a branch of mathematics that deals with vectors and their operations. A vector is a quantity that has both magnitude and direction, and vector algebra pr...read more

Vector Algebra Practice Questions (Medium)

Last Updated: 21 January 2025

Vector Algebra is a branch of mathematics that deals with vectors and their operations. A vector is a quantity that has both magnitude and direction, and vector algebra pr...read more

Practice Questions on Vector Algebra (Hard)

Last Updated: 23 January 2025

Vector Algebra is a branch of mathematics that deals with vectors and their operations. A vector is a quantity with both magnitude and direction, and vector algebra provid...read more

Inner Product on Vector

Last Updated: 10 May 2025

The inner product, also called the dot product, is one of the most fundamental operations in linear algebra. It measures the similarity between two vectors and plays a cru...read more