Cross Product
Define Cross Product.
A cross product is a mathematical operation between two vectors in three-dimensional space, resulting in a third vector that is perpendicular to both input vectors.
Write formula for Cross Product.
Formula for the cross product of two vectors ([Tex]\vec{A}[/Tex]) and ([Tex]\vec{B}[/Tex]) is given by:
[Tex]\vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{vmatrix}[/Tex]
Why cross product is called vector product of two vectors?
The cross product of two vectors results in a new vector perpendicular to the plane formed by the original vectors. Hence, it’s called the vector product.
What is the principle of cross product?
The cross product principle states that the resultant vector is perpendicular to the plane formed by the original vectors and follows the right-hand rule to determine direction.
How to find Cross Product of two vectors?
To find the cross product of two vectors A and B, calculate the determinant of the matrix formed by their components in i, j, and k directions.
What is cross product of two vectors?
Cross product of two vectors, denoted as ([Tex]\vec{A} \times \vec{B}[/Tex]), is a vector that is perpendicular to both input vectors and is normal to the plane containing these vectors. Its magnitude is equal to the product of the magnitudes of the input vectors and the sine of the angle between them.
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