HP (Hewlett-Packard) 50g ユーザーズマニュアル

Page 9-15

equivalent (r,

θ,z) with r = ρ sin φ, θ = θ, z = ρ cos φ.  For example, the following 

figure shows the vector entered in spherical coordinates, and transformed to 
polar coordinates. For this case, 

ρ = 5, θ = 25

o

, and 

φ = 45

o

, while the 

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

∠∠ format in the top 

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 
such that 

ρ = (r

2

+z

2

)

1/2

,

θ = θ, and φ = tan

-1

(r/z).  However, the vector that 

originally was set to Cartesian coordinates remains in that form.   

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

Suppose that a particle is subject to the following forces (in N): F

1

 = 3i+5j+2k,

2

 = -2i+3j-5k, and F

3

 = 2i-3k.  To determine the resultant, i.e., the sum, of all 

these forces, you can use the following approach in ALG mode:

Thus, the resultant is R = F

1

+ F

2

 + F

3

 = (3i+8j-6k)N.   RPN mode use:

[3,5,2] ` [-2,3,-5] ` [2,0,3] ` + +

The angle between two vectors A, B, can be found as 

θ =cos

-1

(A

•B/|A||B|)