Multiply each pair of corresponding components
Add the products together
For vectors (a = (a_1, a_2, dots, a_n)) and (b = (b_1, b_2, dots, b_n)), compute (a_1b_1 + a_2b_2 + dots + a_nb_n)
For 2D vectors ((x_1, y_1)) and ((x_2, y_2)), compute (x_1x_2 + y_1y_2)
For 3D vectors ((x_1, y_1, z_1)) and ((x_2, y_2, z_2)), compute (x_1x_2 + y_1y_2 + z_1z_2)
Check that both vectors have the same number of components