HP 48gII Graphing Calculator Instrukcja Użytkownika Pobierz pdf (Strona 291)

100

101

Page 9-16

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

)

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

= 3i+5j+2k,

= -2i+3j-5k, and F

= 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

+ F

= (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|)

Suppose that you want to find the angle between vectors A = 3i-5j+6k, B =

2i+j-3k, you could try the following operation (angular measure set to degrees)

in ALG mode:

1 - Enter vectors [3,-5,6], press `, [2,1,-3], press `.

2 - DOT(ANS(1),ANS(2)) calculates the dot product

3 - ABS(ANS(3))*ABS((ANS(2)) calculates product of magnitudes

4 - ANS(2)/ANS(1) calculates cos(θ)

5 - ACOS(ANS(1)), followed by ,NUM(ANS(1)), calculates θ

The steps are shown in the following screens (ALG mode, of course):

1 2 ... 286 287 288 289 290 291 292 293 294 295 296 ... 863 864

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