- 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:
CategoryMath