What is the difference between a scalar and a vector?
A scalar is a numerical quantity. .
It has magnitude (size) only.
Examples: A car is moving at 55 miles per hour.. . . . . . . .
A ball is thrown at 30 feet per second.
A vector has magnitude and
Examples: A car is moving at 55 mph to the northeast.. . . . . . . .
A ball is thrown at 30 ft/s at an angle of 50° to the horizontal.
That explanation is only true if the field is (
or subfields of
) and the vector space is a normed space. It doesn't make sense when it is, e.g.,
-vector space, or the space of rational functions of n variables over a field
of positive characteristic.