Snippets Math / Dot Product

Dot Product

By Marcelo Fernandes Jul 09, 2017

Definition:

Dot Product or Scalar Product is an operation that takes two equal-length sequences of numbers and returns a single number.
Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers.

Geometric Meaning:

In Euclidean space, a Euclidean vector is a geometrical object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction that the arrow points. The magnitude of a vector a is denoted by . The dot product of two Euclidean vectors a and b is defined by:

Example:

Calculate the Angle between two vectors u=(2,2,0), v=(0,3,-3).

Following the formula, we get that:
u.v = ||u||*||v||*cos(theta)

6 = sqrt(8)*sqrt(18)*cos(theta)

6 = 2*sqrt(2)*3*sqrt(2)*cos(theta)

cos(theta) = 1/sqrt(2)

theta = 60 degrees.

Notes


Other Formulas:



References:


1 - Wikipedia