Dot Product

Author

Eric W. Weisstein
February 3, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/DotProduct.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/DotProduct.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Identity

(Subscript[A, x])(Subscript[B, x])+(Subscript[A, y])(Subscript[B, y])/.{(Subscript[A, x])->A Cos[(Subscript[θ, A])],(Subscript[A, y])->A Sin[(Subscript[θ, A])],(Subscript[B, x])->B Cos[(Subscript[θ, B])],(Subscript[B, y])->B Sin[(Subscript[θ, B])]}

TrigExpand[A B Cos[(Subscript[θ, A])-(Subscript[θ, B])]]

Multidimensional

With[{n=5},Dot[Array[x,n],Array[y,n]]
]/.a_[b_]:>Subscript[a,b]//TraditionalForm