A typical definition of a vector is stated
as follow:
A vector is a physical quantity that has direction
and magnitude.
This statement is kind of abstract, and can
be confusing for many students.
In reality though, the concept of vector is
very easy, and we use this concept in our
everyday life.
Let me give an example.
Say we want to give directions to go to Angel
Stadium in Anaheim from Cal Poly Pomona.
You could say take Highway 10 and 57.
But this information is not enough because
highway 10 runs from east to west, and we
have to specify which way to go.
East or west.
Similarly 57 runs north-south, and we have
to specify which way to go.
Up north or south.
So the better way to give the direction will
be, take 10 east and then take 57 South.
However, if you think about, this information
is also incomplete.
You can take 10 East but 10 goes all the way
from Santa Monica, CA all the way to Jacksonville,
FL covering almost 4000 Kms.
We don’t want to go that far on 10 east
to take 57 south.
So when do we take the exit for 57 south?
A better way to specify the direction would
be:
Take 10 east, and drive 2 kms
Then take 57 south and drive 35 Kms and you
will reach Angel stadium.
If you look at these statements closely, you
will see we are stating two pieces of information
for each segment.
First 10 East tells you which way to go.
So this gives the direction.
Then 2 Km says how far to go.
So this gives the magnitude.
We can call this quantity as vector because
it has a direction and a magnitude.
So vector is not some difficult concept.
It is a simple concept that we use in our
everyday life when we give directions, or
when even we when we drive our car.
We earlier discussed about forces and force
is also a quantity that has direction and
magnitude.
So force is also a vector.
Examples of vectors are force, position, velocity
and acceleration.
Although these are different physical concepts,
we call them vectors, which make our life
easier.
Now let us see how we can represent a vector.
We can represent vectors by drawing them to
scale.
Drawing vectors is very useful conceptually.
When a vector is represented graphically,
its magnitude is represented by the length
of an arrow and its direction is represented
by the direction of the arrow.
To define the direction, we normally show
the angle, the tail of the vector makes with
the horizontal.
Now that we have a better understanding of
vectors, we are now ready to perform vector
operations such as vector addition.
Vector addition can be done using graphical
and analytical methods.
We will do that in our next video.
