Note the sign of this expression depends only on the angle's cosine, therefore the dot product is
Vector is an object with magnitude and direction. Vector product has lot of application in solving directed graphs.
In Euclidean space, a Euclidean vector is a geometrical object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction the arrow points. The magnitude of a vector A is denoted by ||A||.
Dot product of two Euclidean vectors A and B is defined by
A⋅B=∥A∥∥B∥cosθ,where θ is the angle between A and B.
We can compute (determine) the angle between two vectors, given their coordinates:
cosθ=A⋅B∥A∥∥B∥
A∥∥B∥
Cross product of a vector is an orthogonal vector.