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
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