Application Of Vector Operations; Resultant Of Forces; Angle Between Vectors - HP 49g+ 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|)
Page 9-16  