Law of cosines from dot product. Two vectors A and B originate from a com- mon point. (a) If C = B – A comprises the third side of the triangle, obtain using C · C = (B - A) ·(B – A) the law of cosines relating C to A, B, and the angle a between A and B. (b) Find the expression for the distance from the common point to the side C, in terms of A and B only.

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.