The dot product is a common vector operation with uses in finding perpendicular vectors and leading to vector projections. With the dot product being so useful with vectors, we explore an alteration of the definition called the big-dot product. Given vectors v and u with x as the angle between them, the dot product of vectors v and u is |v||u|sin(x), while the big-dot product with the same givens is |v||u|cos(x). The big-dot product excels with scalar multiples of vectors and areas, but yields a complicated result when finding perpendicular vectors
