HP 50g Graphing Calculator User Manual

Page 290

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Page 9-13

When the rectangular, or Cartesian, coordinate system is selected, the top line
of the display will show an XYZ field, and any 2-D or 3-D vector entered in the
calculator is reproduced as the (x,y,z) components of the vector. Thus, to enter
the vector A = 3i+2j-5k, we use [3,2,-5], and the vector is shown as:

If instead of entering Cartesian components of a vector we enter cylindrical
(polar) components, we need to provide the magnitude, r, of the projection of
the vector on the x-y plane, an angle

θ (in the current angular measure)

representing the inclination of r with respect to the positive x-axis , and a z-
component of the vector. The angle

θ must be entered preceded by the angle

character (

∠), generated by using ~‚6. For example, suppose that we

have a vector with r = 5,

θ = 25

o

(DEG should be selected as the angular

measure), and z = 2.3, we can enter this vector in the following way:

„Ф5 ‚н ~‚6 25 ‚н 2.3

Before pressing

`, the screen will look as in the left-hand side of the

following figure. After pressing

`, the screen will look as in the right-hand

side of the figure (For this example, the numerical format was changed to Fix,
with three decimals).

Notice that the vector is displayed in Cartesian coordinates , with components
x = r cos(

θ), y = r sin(θ), z = z, even though we entered it in polar coordinates.

This is because the vector display will default to the current coordinate system.
For this case, we have x = 4.532, y = 2.112, and z = 2.300.

Suppose that we now enter a vector in spherical coordinates (i.e., in the form
(

ρ,θ,φ), where ρ is the length of the vector, θ is the angle that the xy projection

of the vector forms with the positive side of the x-axis, and

φ is the angle that ρ

forms with the positive side of the z axis), with

ρ = 5, θ = 25

o

, and

φ = 45

o

.

We will use:

„Ф5 ‚н ~‚6 25 н

~‚6 45

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