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Different ways of representing the group $SU(3)$ within a Geometric Algebraapproach are explored. As part of this we consider characteristic multivectorsfor $SU(3)$, and how these are linked with decomposition of generators intocommuting bivectors. The setting for this work is within a 6d EuclideanClifford Algebra. We then go on to consider whether the fundamental forces ofparticle physics might arise from symmetry considerations in just the 4dgeometric algebra of spacetime -- the STA. As part of this, a representation of$SU(3)$ is found wholly within the STA, involving preservation of a bivectornorm. We also show how Octonions can be fully represented within the SpacetimeAlgebra, which we believe will be useful in making them understandable andaccessible to a new community in Physics and Engineering. The two strands ofthe paper are drawn together in showing how preserving the octonion norm is thesame as preserving the timelike part of the Dirac current of a particle. Thissuggests a new model for the symmetries preserved in particle physics.Following on from work by G\"unaydin and G\"ursey on the link between quarks,and octonions, and by Furey on chains of octonionic multiplications, we showhow both of these fit well within our scheme, and give some wholly STA versionsof the operations involved, which in the cases considered have easilyunderstandable equivalents in terms of 4d geometry. Links with larger groupscontaining $SU(3)$, such as $G_2$ and $SU(8)$, are also considered.

Some recent results for $SU(3)$ and Octonions within the Geometric Algebra approach to the fundamental forces of nature