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

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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