How do I find the dot product of two 3-dimensional vectors

Example; Let vector v = (2,5,2) and vector u = (1,-2,3),then u · v = [(2 x 1) + (5 x -2) + (2 x 3)] = [2 -10 + 6] = -2 As the workings hopefully make clear in the line above, the general formula for the scalar product of vectors a and b (if a = (x₁,y₁,z₁) and b = (x₂,y₂,z₂)) is 𝒂∙𝒃=(𝒙₁𝒙₂+ 𝒚₁𝒚₂+𝒛₁𝒛₂). The same holds true if the vectors are represented as column vectors. If the angle between two vectors is known, it is also possible to calculate the scalar product using the equation: 𝒖∙𝒗=𝑼𝑽𝒄𝒐𝒔(𝜽) where U and V are the magnitudes of u and v and 𝜽 is the angle between the vectors. *Note, the scalar product of two perpendicular vectors is 0 as cos(90°)=0