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Scalars and Vectors

We can classify physical quantities as scalars or vectors. The basic difference is that a direction is associated with a vector but not with a scalar.

A scalar quantity has magnitude only. It is specified by a single number, with the proper unit. For example,the mass of an object, the temperature of a body,the distance between two points, and the time at which a certain event happened are scalars. Scalars follow the rules ofordinary algebra. That means scalars can be added, subtracted, multiplied, and divided like basic numbers.

A vector is a physical quantity that has both magnitude and direction. It should also obey the triangle law of vector addition or equivalently the parallelogram law of vector addition. Therefore a vector is specified by giving its magnitude by a number and its direction. Some examples of vectors are displacement, acceleration,velocity, and force.

To represent a vector, we use boldface or arrow. Thus, a force vector can be represented by a symbol  or .

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