# Application Of Vector Operations; Angle Between Vectors; Resultant Of Forces - HP 50g User Manual

Graphing calculator.

equivalent (r, ,z) with r =
figure shows the vector entered in spherical coordinates, and transformed to
polar coordinates. For this case,
transformation shows that r = 3.563, and z = 3.536. (Change to DEG):
Next, let's change the coordinate system to spherical coordinates by using
function SPHERE from the VECTOR sub-menu in the MTH menu. When this
coordinate system is selected, the display will show the R
line. The last screen will change to show the following:
Notice that the vectors that were written in cylindrical polar coordinates have
now been changed to the spherical coordinate system. The transformation is
2
such that
= (r
originally was set to Cartesian coordinates remains in that form.

## Application of vector operations

This section contains some examples of vector operations that you may
encounter in Physics or Mechanics applications.

### Resultant of forces

Suppose that a particle is subject to the following forces (in N): F
F
= -2i+3j-5k, and F
2
these forces, you can use the following approach in ALG mode:
Thus, the resultant is R = F
[3,5,2] ` [-2,3,-5] ` [2,0,3] ` + +

### Angle between vectors

The angle between two vectors A, B, can be found as
sin ,
2
1/2
+z
)
,
= , and
= 2i-3k. To determine the resultant, i.e., the sum, of all
3
+ F
1
2
= , z =
cos . For example, the following
o
= 5,
= 25
, and
-1
= tan
(r/z). However, the vector that
+ F
= (3i+8j-6k)N. RPN mode use:
3
o
= 45
, while the
format in the top
= 3i+5j+2k,
1
-1
=cos
(A B/|A||B|)
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