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Cross-multiplication is a shortcut, an easily understandable procedure that can be taught to students. Use. This is a common procedure in mathematics, used to reduce ...
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
Multiplication (often denoted by the cross symbol , by the mid-line dot operator ⋅, by juxtaposition, or, on computers, by an asterisk *) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division.
There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar , while the cross product [ a ] returns a pseudovector . Both of these have various significant geometric interpretations and are widely used in mathematics, physics , and engineering .
Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle ...
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
The word cross is recorded in 11th-century Old English as cros, exclusively for the instrument of Christ's crucifixion, replacing the native Old English word rood.The word's history is complicated; it appears to have entered English from Old Irish, possibly via Old Norse, ultimately from the Latin crux (or its accusative crucem and its genitive crucis), "stake, cross".
[7] [8] Euclid is known to have assumed the commutative property of multiplication in his book Elements. [9] Formal uses of the commutative property arose in the late 18th and early 19th centuries, when mathematicians began to work on a theory of functions.