Are there have three vector that multiply to form scaler quantity like volumn is volume is the product of three vector
Answers
Examples of vector quantities include displacement, velocity, position, force, and torque. The scalar triple product of three vectors a, b, and c is (a×b)⋅c. ... The scalar triple product is important because its absolute value |(a×b)⋅c| is the volume of the parallelepiped spanned by a, b, and c (i.e., the parallelepiped whose adjacent sides are the vectors a, b, and c). It can be expressed in terms of the magnetic moment of the system, by expanding the vector triple product: K = ∑ e c { v ( r · H ) − H ( v · r ) } = ∑ e c { v ( r · H ) − 1 2 H d d t r 2 } . (67.1) We call attention to the analogy with formula (64.6) for the electrical case. (a x b) x c = (a c)b - (b c)a (1) for the repeated vector cross product. This vector-valued identity is easily seen to be. completely equivalent to the scalar-valued identity. (a x b) (c x d) = (a c)(b d) - (a d)(b c).