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vectors

continuation of vectors Vectors, phosphors  and the combination of  waveform 21.1 Introduction Some physical quantities are entirely defined by a numerical value and are called scalar quantities or scalars. Examples of scalars include time, mass, temperature, energy and volume. Other physical quantities are defined by both a numerical value and a direction in space and these are called vector quantities or vectors. Examples of vectors include force, velocity, moment and displacement. 21.2 Vector addition A vector may be represented by a straight line, the length of line being directly proportional to the magnitude of the quantity and the direction of the line being in the same direction as the line of action of the quantity. An arrow is used to denote the sense of the vector, that is, for a horizontal vector, say, whether it acts from left to right or vice-versa. The arrow is positioned at the end of the vector and this position is called the ‘nose’of the vector.
A vector may be defined as a directed quantity which obeys a certain rule of operation r = a + b   Scalars are common algebraic magnitudes,