I
NTRODUCTION
TO
V
ECTORS
A
scalar
is a quantity that has magnitude but no direction.
You can have signed scalar
quantities as well.
A
vector
is a quantity that has
both
magnitude
and direction
.
Some examples of scalar quantities are length, temperature (signed), and mass.
Some
examples of vector quantities are force, acceleration, displacement, and velocity.
To specify the velocity of a moving point in the coordinate plane, we must give both the rate
at which the point moves (speed) and the direction of that motion.
The velocity vector
incorporates both pieces of information.
The length of the vector represents its magnitude
and its direction is represented by the direction of the arrow that represents the vector.
A vector
u
is represented in boldface, but for our purposes, we will use
u
.
There are a
number of different ways to express a vector.
When we describe vectors, it is usual to do so by expressing them in terms of a
basis
.

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