In physics problems, it is important to recognize when working with scalar or vector operations, as this can dramatically change the results. Scalar quantities are given by a data point, such as temperature, whereas vector quantities are given in a three-dimensional space, such as velocity. Preforming mathematical operations to a scalar quantity is simple. Just carry out the operation as normal and carry and convert the units. A vector quantity requires the direction of the vector to be taken into consideration.
Scalar quantities only deal with the magnitude of the medium. Scalar quantities is generally what is used. Time, volume, speed and temperature are common scalar quantities. They are just a data point with no respect to any direction. Vector quantities are what indicate direction and can become more complex in the mathematical computation. Increase/Decrease in temperature and velocity are common examples of vector quantities. It is possible to multiply a scalar and vector quantity together. The resulting quantity will be a vector.