HP 48gII - Manual (Page 277)

Page 9-2
There are two definitions of products of physical vectors, a scalar or internal
product (the dot product) and a vector or external product (the cross product).
The dot product produces a scalar value defined as
A•B = |A||B|cos(θ),
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: