Torque the vector cross product, p is the particle's linear momentum, and r is the displacement vector from the origin (the origin is assumed to be a fixed location anywhere in space). The time-derivative of this is: This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definition of force formula_17 (whether or not mass is constant) and the definition of velocity formula_18 The cross product of momentum formula_20 with its associated velocity formula_21 is zero because velocity and momentum are parallel, so the second term vanishes. By definition, torque τ
Cross product formula_123 is its velocity and formula_124 is the body's angular velocity. Since position formula_110 and velocity formula_123 are "true" vectors, the angular velocity formula_124 is a "pseudovector" or "axial vector". The cross product is used to describe the Lorentz force experienced by a moving electric charge formula_128: Since velocity formula_123, force formula_118 and electric field formula_132 are all "true" vectors, the magnetic field formula_133 is a "pseudovector". In vector calculus, the cross product is used to define the formula for the vector operator curl. The trick of rewriting a cross product in terms of a matrix multiplication appears frequently in