Scalar Product of Vectors

The scalar product of vectors is also a scalar quantity, its value can be calculated using the formula a x b = |a| x |b| x cos α. In another variant, the calculation of the product of vectors on the plane is performed by pairwise multiplication of the vector coordinates a • b = ax x bx + ay x by. For example, for 2 vectors with coordinates a = {3; 5} and b = {4; 3} the scalar product will be equal to 3 x 4 + 5 x 3 = 27.

In the case of considering the scalar product of vectors located in a coordinate system XYZ, a = {ax ; ay ; az} and b = {bx ; by ; bz} the calculation is performed using formulas similar to the planar variant. a • b = ax x bx + ay x by + az x bz.

For example, for 2 vectors with coordinates a = {3; 5; 2} and b = {4; 3; 5} the scalar product will be equal to 3 x 4 + 5 x 3 + 2 x 5 = 37.

General for n-dimensional space the calculation formula will be as follows: a • b = a1 x b1 + a2 x b2 + ... + an x bn.