HP 48gII - Manual (Page 291)

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