# Application Of Vector Operations; Resultant Of Forces; Angle Between Vectors - HP 48gII User Manual

Graphing calculator.

Notice that the vectors that were written in cylindrical polar coordinates have
now been changed to the spherical coordinate system. The transformation is
2
2
1/2
such that ρ = (r
, θ = θ, and φ = tan
+z
)
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
= 2i-3k. To determine the resultant, i.e., the sum, of all
2
3
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 θ =cos
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
(r/z). However, the vector that
+ F
+ F
= (3i+8j-6k)N. RPN mode use:
1
2
3
= 3i+5j+2k,
1
-1
(A•B/|A||B|)
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