Application of Cross Product

Application of cross product are as follow:

  • Torque calculation in physics and engineering, where it’s used to determine rotational force.
  • Magnetic field calculation in electromagnetism, where it helps find the direction of magnetic fields around current-carrying wires.
  • Angular momentum calculation in rotational motion problems, indicating the rotational motion’s intensity.
  • Essential in vector algebra for determining perpendicular vectors and calculating areas of parallelograms.
  • Crucial in computer graphics for determining surface normals, aiding in realistic lighting effects in 3D rendering.

Some Important Results

  • Area of a Parallelogram with adjacent sides [Tex]\vec{a}[/Tex] and [Tex]\vec{b}[/Tex] is [Tex]|\vec{a}×\vec{b}|[/Tex]
  • Area of a Triangle with adjacent sides [Tex]\vec{a}[/Tex] and [Tex]\vec{b}[/Tex] is [Tex]1/2|\vec{a}×\vec{b}|[/Tex]

Cross Product

Cross product or vector product is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space. Cross product, also called the vector cross product, is a mathematical operation performed on two vectors in three-dimensional space.

In this article, we will understand the meaning of cross product, its definition, the formula of the cross product, the cross product of perpendicular vectors, the cross product of parallel vectors, the right-hand rule cross product and the properties of the cross product.

Table of Content

  • What is Cross Product?
  • Formula of Cross Product
  • Cross Product of Perpendicular Vectors
  • Cross Product of Parallel Vectors
  • Right-Hand Rule Cross Product
  • Matrix Representation of Cross Product
  • Triple Cross Product
  • Cross Product Properties
  • Application of Cross Product

Similar Reads

What is Cross Product?

Cross-product is a mathematical operation that takes two vectors in three-dimensional space and produces a third vector that is perpendicular to both input vectors. It is denoted by the symbol “×” and is used to calculate the area of a parallelogram formed by the two vectors and the direction of the resulting vector is determined by the right-hand rule....

Formula of Cross Product

Formula for cross product of two vectors ([Tex]\vec{A}[/Tex]) and ([Tex]\vec{B}[/Tex]) in three-dimensional space is:...

Right-Hand Rule for Cross Product

Right-hand rule is a convention used to determine the direction of the resulting vector when performing a cross product....

Matrix Representation of Cross Product

Cross product of two vectors can also be represented using a matrix....

Triple Cross Product

Triple cross product is a mathematical operation involving three vectors in three-dimensional space. Given three vectors ([Tex]\vec{A}[/Tex]), ([Tex]\vec{B}[/Tex]), and ([Tex]\vec{C}[/Tex]), the triple cross product is denoted as ([Tex]\vec{A} \times \vec{B}) \times \vec{C}[/Tex])....

Cross Product Properties

The various properties of cross product are listed below:...

Cross Product vs Dot Product

Cross product and dot product are two types of product operation defined on vectors with each resulting in vector and scaler output respectively. Some of the common differences between cross and dot product are:...

Application of Cross Product

Application of cross product are as follow:...

Examples on Cross Product

Example 1: Calculate the cross product of the vectors ([Tex]\vec{A}[/Tex] = ❬ 2, -1, 3 ❭) and ([Tex]\vec{B}[/Tex] = ❬ -3, 4, 1 ❭)....

Practice Questions on Cross Product

Q1: Given two vectors ( [Tex]\vec{A} [/Tex]= ❬ 1, 2, -3 ❭) and ( [Tex]\vec{B}[/Tex] = ❬ 2, -1, 4 ❭ ), find ( [Tex]\vec{A} \times \vec{B} [/Tex])....

FAQs on Cross Product

Define Cross Product....

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