Application of vector operations, Resultant of forces, Angle between vectors – HP 50g Graphing Calculator User Manual

Page 292: Application of vector operations ,9-15

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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.

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

1

= 3i+5j+2k,

F

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] ` + +

Angle between vectors

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

θ =cos

-1

(A

B/|A||B|)

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