Dot Product

Geometrically:

The Dot Product of two unit-length vectors is defined to be the cosine of the angle between them. For more general vectors, the Dot Product is defined to be linear in vector lengths.

Algebraically:

The Dot Product of two vectors is the sum of the products of corresponding terms.

Examples:

• [1,2].[4,5] = 1*4+2*5 = 14
• [1,2,3].[-3,6,-3] = 0
  • This shows that geometrically these two vectors are perpendicular.

The connection between the algebraic and geometric interpretations leads to some extremely useful methods of calculation.

See also:

• http://mathworld.wolfram.com/DotProduct.html
• DotProductInManyProgrammingLanguages

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CategoryMath