VECTOR PRODUCT Meaning and
Definition
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The vector product, also known as the cross product, is a mathematical operation performed on two vectors in three-dimensional space to generate a new vector. It is denoted by the symbol "×" or simply by the use of a bold "x".
The vector product between two vectors, typically denoted as A and B, is computed as follows: A × B = C. The resulting vector C is perpendicular to both A and B, and its magnitude is given by the product of the magnitudes of A and B multiplied by the sine of the angle between them. This means the vector product is non-commutative, meaning that A × B is not the same as B × A.
Geometrically, the vector product can be visualized using the right-hand rule. If the fingers of the right hand are curled from the direction of A to B, then the thumb points in the direction of C, following the order of the cross product. This allows for determining the direction of the resulting vector.
The vector product possesses several important properties, such as linearity, distributivity, and anticommutativity. It finds widespread use in various fields, including physics, engineering, and computer graphics. It is employed to calculate torque, angular momentum, magnetic fields, and to model the motion of objects in three-dimensional space. Overall, the vector product plays a crucial role in understanding and solving problems involving vectors in a three-dimensional coordinate system.
Common Misspellings for VECTOR PRODUCT
- cector product
- bector product
- gector product
- fector product
- vwctor product
- vsctor product
- vdctor product
- vrctor product
- v4ctor product
- v3ctor product
- vextor product
- vevtor product
- veftor product
- vedtor product
- vecror product
- vecfor product
- vecgor product
- vecyor product
- vec6or product
Etymology of VECTOR PRODUCT
The etymology of the word "vector" can be traced back to the Latin word "vector", which means "carrier" or "bearer". It originated from the verb "vehere", meaning "to carry" or "to convey". The term "vector" in its mathematical sense was introduced by British mathematician William Rowan Hamilton in the mid-19th century.
The term "product" comes from the Latin word "producere", meaning "to bring forth" or "to produce". In mathematics, a product refers to the result of multiplying two or more numbers or quantities.
When these two terms are combined to form "vector product", it refers to a mathematical operation that produces a new vector from two given vectors. This operation is also known as the cross product, as it is represented by a cross symbol ('×') in mathematical notation.
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