Look at this example that shows a force in
3D.
The force F makes an angle theta sub x with
x-axis, theta sub y with y-axis and theta
sub z with z axis.
If you know these three angles, you can easily
find the components of this force on each
axis.
For example, the x-component of this force
is the magnitude of this force times the cosine
theta sub x.
You can do this for each axis.
The y-component of this force is the magnitude
of this force times the cosine theta sub y
and so on.
The angles theta sub x, theta sub y and theta
sub z define the direction of the force, so
the cosines of these angles are known as direction
cosines.
Solving problems using direction cosines is
a nice, elegant approach.
Unfortunately, these angels are not commonly
available in real problems.
Look at the flower pot problem that we discussed
earlier.
How do we find the these cosine angles?
We can assume that the three forces carry
equal load and make the same angle with the
vertical y-axis.
But we still don’t know the other angles,
angle with x-axis and z-axis for each force.
The only way to find these angles is for someone
to physically measure, or calculate.
So, for even a simple problem like this one,
the angles between a force and each of the
axis is not readily available.
In such cases, we may want to explore other
approaches.
