Products {scalar product}| {dot product} {inner product} of two vectors can result in scalars. Scalar product sign is bold dot: u . v, where u and v are vectors.
Scalar equals first vector-length u times second-vector length v times cosine of angle A between vectors: |u| * |v| * cos(A).
Scalar equals first-vector first coordinate x1 times first-vector second coordinate x2 plus second-vector first coordinate y1 times second-vector second coordinate y2: x1 * x2 + y1 * y2.
Both vectors can be the same: x*x + y*y = x^2 + y^2. Two vectors are parallel if they are scalar multiples. Two vectors are perpendicular if their scalar product equals zero.
Scalar product is commutative, is distributive, and has no inverse. Scalar products find energies and so where functions begin or end (boundaries).
Mathematical Sciences>Calculus>Vector>Operations>Product
3-Calculus-Vector-Operations-Product
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Date Modified: 2022.0224