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.
The dot product can be defined for two vectors and by. (1). where is the angle between the vectors and is the norm. It follows immediately that if is perpendicular to. The dot product therefore has the geometric interpretation as the length of the projection of onto the unit vector when the two vectors are placed so that their tails coincide.