A car starts from a garage, goes towards South through a distance of 3km and then turns towards West, moves further through a distance of 4 km, and finally comes straight to the garage and stops. What is the displacement made by the car in this journey? What's about the distance traveled by the car? The answer to the first question is zero and the answer to the second question is 12km. This simple example gives an idea of two kinds of physical quantities - vectors and scalars.
A vector quantity is the quantity which requires magnitude and direction both to specify it completely. On the other hand, a scalar quantity has only a magnitude, but no direction. In the example of the opening paragraph, therefore, displacement is a vector quantity but distance is a scalar quantity. Similarly, speed is a scalar where as velocity is a vector. Mass, time, electric potential, etc., are some other examples of scalars. Force or weight, acceleration, electric field, etc., are some examples of vectors.
A vector is represented by a letter with an arrow on top of it or a bold-faced letter in print. A scalar, on the other hand, is represented by an ordinary letter (no bold-faced) without arrow on it. Scalars follow algebraic rules in addition and multiplication but some specific rules should be followed while adding and multiplying two vectors.
Test yourself
(1) Your friend started to walk from the campus center, moved towards South through 6 steps and then towards East through 8 steps. What is her displacement in this motion? What's about the distance covered by her?
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