MULTIVECTOR OPERATIONS (a.k.a. GEOMETRIC ALGEBRA OR CLIFFORD ALGEBRA OPERATIONS). PLEASE SEE New Foundations of Mechanics , D. Hestenes, ONLINE CITATIONS BELOW, AND "CLIFFORD" WEBSITES.
INNER (a.k.a. SCALAR) PRODUCT: [a1,a2] · [b1 , b2] = a1 * b1 + a2 * b2, A SCALAR. For plain triangle with its Law of Cosines; as triangle becomes vector triangle, Cosine Law becomes INNER PRODUCT.
VECTOR A

VECTOR B

SCALAR C

INNER PRODUCT:A o B = a1* b1 + a2* b2
OUTER PRODUCT