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Example definitions and formulas using three-dimensional vector representation of two weight vectors expand Edit this paragraph Example 1 , electromagnetics ,2013 Football Boots Soccer Cleats Shoes Nike Mercurial Vapor VIII Superfly Fourth CR Black Green , known current direction and the direction of magnetic field lines , find the direction of the force , it is necessary to use fork multiply . 2 , statics , the known magnitude and direction of the force point of the shaft to the distance and direction , the direction of torque demand ,Football Boots Messi 7 Adidas F50 adizero TRX FG TPU Leather Silver Black Blue , to use the fork by editing the section definition and formula for the cross product , also called the outer product of vectors , the vector product . As the name implies , seeking down result is a vector , denoted by the vector c. Two vectors a and b, the cross product of writing a × b ( sometimes written as a ∧ b, to avoid confusion and the letter x ) . Vector product can be defined as : | vector c | = | a × vector vector b | = | a | | b | sinθ where θ represents the angle between the two vectors angle (0 ° ≤ θ ≤ 180 °), it perpendicular to both the plane defined by the vector can be determined with the right-hand rule . ( Note : a × b is not writing a · b, represent the two different algorithms , the former fork by the latter dot ) method using the direction vector c and a, b ​​perpendicular to the plane and the direction use the " right-hand rule " to judge . Judgment as follows: 1 . Hand palm open , four fingers close together, thumb pointing perpendicular to the direction of four fingers ; 2 . Stretched out his right hand , four fingers bent, rotated four fingers with the A to B in the same direction , then the thumb pointing to C vectors. Thus, the outer product of vector multiplication exchange rate of non-compliance , as vectors a × vector b = - b × vector a vector in physics , known force and torque arm seeking is the outer product of vectors that cross product . A three-dimensional vector representation of the vector with the coordinates ( three-dimensional vectors ) , if the vector a = (a1, b1, c1), vector b = (a2, b2, c2), vectors of the vector a · b = a1a2 + b1b2 + c1c2 Vector a × vector b = | ijk | | a1 b1 c1 | | a2 b2 c2 | is a value of a third-order determinant (b1c2-b2c1, c1a2-a1c2, a1b2-a2b1) (i,2013 Football Boots Soccer Cleats Shoes WholeNike CTR360 Maestri II Elite FG Leather Red White Black , j, k are the spatial in the three mutually perpendicular axes unit vectors ) . Two due to heavy weight vector vector cross multiplication calculation is more complicated , so directly gives the following simplified formulas and proofs :

weight vector cross product of two simple formulas and prove