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The CrossProduct
We live in a threedimensional universe. Those three dimensions can be distinguished as
right/left, up/down, and forward/back, or as
±x
,
±y
, and
±z
, each being perpendicular to
the other two. The
crossproduct
is a function akin to multiplication that takes vectors
along two dimensions and yields a quantity in the third by the RightHand Rule (RHR).
Generically, the crossproduct acting on a pair of vectors is written
!
A
!
!
B
. The result will
be a vector, not a simple scalar value like the dotproduct would yield. If you happen to
know the magnitudes of the two vectors and the angle between them, the cross product
can be computed using
AB
sin
θ
. The direction is then found from RHR. For instance,
suppose the pair of vectors shown occur in a problem and you
are asked to find “AcrossB”. The magnitude would be
(6)(3)
30°=9
. The direction going from
!
A
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This note was uploaded on 04/05/2012 for the course PHYS 131 taught by Professor Tibbets during the Spring '11 term at Cuyamaca College.
 Spring '11
 Tibbets

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