Dot Product; Cross Product; Decomposing A Vector - HP 50g User Manual

Graphing calculator.

Dot product

Function DOT is used to calculate the dot product of two vectors of the same
length. Some examples of application of function DOT, using the vectors A, u2,
u3, v2, and v3, stored earlier, are shown next in ALG mode. Attempts to
calculate the dot product of two vectors of different length produce an error
message:

Cross product

Function CROSS is used to calculate the cross product of two 2-D vectors, of two
3-D vectors, or of one 2-D and one 3-D vector. For the purpose of calculating a
cross product, a 2-D vector of the form [A
, A
], is treated as the 3-D vector [A
,
x
y
x
A
,0]. Examples in ALG mode are shown next for two 2-D and two 3-D vectors.
y
Notice that the cross product of two 2-D vectors will produce a vector in the z-
direction only, i.e., a vector of the form [0, 0, C
]:
z
Examples of cross products of one 3-D vector with one 2-D vector, or vice versa,
are presented next:
Attempts to calculate a cross product of vectors of length other than 2 or 3,
produce an error message (Invalid Dimension), e.g., CROSS(v3,A), etc.

Decomposing a vector

Function V
is used to decompose a vector into its elements or components. If
used in the ALG mode, V
will provide the elements of the vector in a list, e.g.,
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