Dot Products and Cross Products

Normal vector (to a plane)

A vector that is perpendicular to plane in question

Law of Cosines

C^2 = A^2 + B^2 - 2ABcos@

Cauchy Schwarz Inequality

For any two nonzero vectors in R^n, the absolute value of their dot product is less than or equal to the product of the lengths of the vectors

Triangle Inequality

For any two nonzero vectors in R^n, the length of the sum of the two vectors is less than or equal to the sum of the lengths of each of the vectors

Magnitude/Norm

Length of a vector

Right Hand Rule

Position your right hand so that your fingers point in the direction of V (index finger on V) and the palm faces toward W. Wherever your thumb points is the direction of V x W.

Length (of a vector)

Sqrt(V1^2+V2^2+...+Vn^2)

Perpendicular

The angle between two nonzero vectors is a right angle. The dot product of the two vectors is also 0, and cos(angle)=0.

Orthogonal

The dot product of two vectors is 0

Dot Product

Vector multiplication operation in which you multiply corresponding components of two vectors and add them to products of other corresponding components.

Unit Vector

Vector with length 1