A scalar is a quantity
that is completely specified by its magnitude and has no direction. A scalar can
be described either dimensionless, or in terms of some physical quantity. Examples
of scalars are: mass, volume, distance, energy, and time. Scalar
quantities can be manipulated by the laws of arithmetic applicable to natural
numbers. For example if I add 20 grams of sugar to a recipe and then add 20 grams
more the result is 40 grams of sugar in the recipe. If I buy a liter (1000ml)
bottle of water and drink 250 ml, the amount left over is 750 ml.
A vector
is a quantity that specifies both a magnitude and a direction.
Such a quantity may be represented geometrically by an arrow
of length proportional to its magnitude, pointing in the assigned
direction. Examples of vectors are: displacement, velocity,
acceleration, force and electric field. Vectors can be added
in simple ways that scalars can. For example: A plane flies
south at 500 miles/hour. A wind blows from the east at 100 miles/hour
occurs. The resultant speed is not 600 miles/hour or 400 miles
per hour.
  The
resultant (red arrow) can be calculated using the Pythagorean Theorem R=
sqrt (100^2 + 500^2) R=
509.9 mi/hr. The
direction of the plane can be calculated using the cosine function. tan
= 100/500 = 11.31 degrees (Note:
diagram is not drawn to scale) 
