What is Cross Product of Two Vectors?
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.
Cross Product Definition
Cross product of two independent vectors, A and B, denoted as A × B, yields a new vector that is perpendicular to both A and B and is normal to the plane containing these vectors.
Magnitude of the cross product is given by the product of the magnitudes of A and B and the sine of the angle θ between them.
Symbolically, if A = |A| and B = |B|, the cross product is expressed as:
[Tex]\vec{A} \times \vec{B} = |\vec{A}| \cdot |\vec{B}| \cdot \sin \theta ~\hat{n}[/Tex]
If two vectors lie in the X-Y plane, their cross-product results in a vector along the Z-axis, perpendicular to the XY plane. The symbol “×” is used between the original vectors, and the resultant vector is represented as ([Tex]\vec{c}[/Tex]) in the equation ([Tex]\vec{a} \times \vec{b} = \vec{c}[/Tex]).
Cross-Product
Cross Product of Two Vectors
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 of Two Vectors?
- Formula of Cross-Product
- Right-Hand Rule for Cross-Product
- Matrix Representation of Cross-Product
- Triple Cross Product
- Cross Product Properties
- Application of Cross-Product of Two Vectors