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.