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.
This is a pretty simple proof. Letâs start with and compute the dot product. Now, since we know for all i then the only way for this sum to be zero is to in fact have . This in turn however means that we must have and so we must have had .