Trigonometry/Vectors and Dot Products

thumb|230px|Calculating bond angles of a symmetrical tetrahedral molecule such as methane using a dot product Consider the vectors U and V (with respective magnitudes |U| and |V|). If those vectors enclose an angle θ then the dot product of those vectors can be written as: If the vectors can be written as: then the dot product is given by: For example, and We can interpret the last case by noting that the product is zero because the angle between the two vectors is 90 degrees. Since and this means that Trigonometric Form of the Complex Number Vectors in the Plane