The dot product (or inner product)
of two vectors
a1, a2,..., an
and
b1, b2,..., bn
is defined by
For the following examples of dot products with n = 3, define
Evaluate
u, v, w
⋅
x, y, z
= ux + vy + wz
(1, 2, 3)⋅(3, 2, 1) = 10
a⋅c = 10
a⋅b = - 2
c⋅d = 4