Diabetes happens when one of the following occurs: 1  When the pancreas does not produce any insulin. 2  When the pancreas produces very little insulin. 3  When the body does not respond appropriately to insulin, a condition called insulin resistance..
Vector Calculus: Understanding the Dot Product. Think of the dot product as directional multiplication. Multiplication goes beyond repeated counting: it's applying the essence of one item to another. Complex multiplication combines rotations.
Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.