Vector algebra relations

Abstract: The Sine Dot Product is an original study introduced by the author into the mathematical domain. The main goal of introducing this new study is to find applications and to facilitate many complicated issues that are difficult to resolve using the traditional Vectorial product (Cross Product) and the Dot product. The idea of the Sine Dot Product is to multiply two vectors and the result will be a Scalar equal to the magnitude of the two vectors multiplied by sine instead of cosine. In this paper, a brief study is introduced with the definition of the Sine Dot Product and simple applications are developed as the Magnitude of the Sine Dot Product will give the Area of the two vectors, moreover one can find the equation of a plane in 3-Dimensions using the Sine DotProduct. The method of using the Sine Dot Product instead of the Cross Product and Dot Product is much easier to find the equation of a plane in 3-Dimensions. Many studies will follow this one in order to find more important applications of this new Product between vectors.