Suppose we have two arrows.
Let us define the cross product of these two arrows to be a third arrow.
The arrow representing the cross product
is always exactly 90 degrees to the two original arrows.
The length of the arrow representing the cross product
is always exactly equal to the area of the parallelogram
that is formed by the original two arrows.
The cross product of two arrows plays a critical role
in many areas of science and engineering.
Another type of calculation that plays a critical role
is what we refer to as the dot product of two arrows.
The first arrow defines a line.
This line and the second arrow form a triangle.
Consider the length of this side of the triangle.
Now, consider this length multiplied by the length of the first arrow.
The result of this multiplication is what we refer to as the dot product.
If the first arrow and the red arrow are pointed in opposite directions,
then the dot product is negative.
Whereas the cross product of two arrows is another arrow,
the dot product of two arrows is just a number.
Whenever we take the dot product of two arrows, we will
always get the same answer regardless of
which of the two arrows we refer to as the first arrow,
and which of the two arrows we refer to as the second arrow.
This is not the case with cross product.
If we reverse the order of the two original arrows,
then the arrow for the cross product will end up pointing in the opposite direction.
There is a rule for using your right hand to remember
the direction in which the arrow representing the cross product is pointing.
If you point your right hand in the direction of the first arrow,
and then curl your fingers in the direction of the second arrow,
your thumb will end up pointing in the direction of the cross product.
Much more information is available in the other videos on this channel,
and please subscribe for notifications when new videos are ready.