HP 50g Graphing Calculator - Manual (Page 279)

Page 9-2
where θ is the angle between the two vectors. The cross product produces a
vector A ×B whose magnitude is |A×B| = |A||B|sin(θ), and its direction is
given by the so-called right-hand rule (consult a textbook on Math, Physics, or
Mechanics to see this operation illustrated graphically). In terms of Cartesian
components, A
•B = A
x
B
x
+A
y
B
y
+A
z
B
z
, and A ×B = [A
y
B
z
-A
z
B
y
,A
z
B
x
-A
x
B
z
,A
x
B
y
-
A
y
B
x
]. The angle between two vectors can be found from the definition of the
dot product as cos( θ) = A•B/|A||B|= e
A
•e
B
. Thus, if two vectors A and B
are perpendicular ( θ = 90 0
= π/2 rad
), A •B = 0.
Entering vectors
In the calculator, vectors are represented by a sequence of numbers enclosed
between brackets, and typically entered as row vectors. The brackets are
generated in the calculator by the keystroke combination
„Ô , associated
with the * key. The following are examples of vectors in the calculator:
[3.5, 2.2, -1.3, 5.6, 2.3] A general row vector
[1.5,-2.2] A 2-D vector
[3,-1,2] A 3-D vector
['t','t^2','SIN(t)'] A vector of algebraics
Typing vectors in the stack
With the calculator in ALG mode, a vector is typed into the stack by opening a
set of brackets (
„Ô) and typing the components or elements of the vector
separated by commas ( ‚í). The screen shots below show the entering of
a numerical vector followed by an algebraic vector. The figure to the left shows
the algebraic vector before pressing
„. The figure to the right shows the
calculator’s screen after entering the algebraic vector:
In RPN mode, you can enter a vector in the stack by opening a set of brackets
and typing the vector components or elements separated by either commas
(
‚í) or spaces (#). Notice that after pressing ` , in either mode,
the calculator shows the vector elements separated by spaces.