Difference between revisions of "Dot product"
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It follows from the above definition that the dot product of X and Y is 0 if X is perpendicular to Y. | It follows from the above definition that the dot product of X and Y is 0 if X is perpendicular to Y. | ||
| − | Alternatively, one can describe the dot product as the length of the geometric | + | Alternatively, one can describe the dot product as the length of the geometric projection of X onto the unit vector Y when the tails of the two vectors are placed at the same point. |
[[category:mathematics]] | [[category:mathematics]] | ||
[[category:physics]] | [[category:physics]] | ||
Revision as of 19:08, December 26, 2007
The dot product is defined for two vectors X and Y to be:
where |x| is the norm and theta is the angle between the vectors.
It follows from the above definition that the dot product of X and Y is 0 if X is perpendicular to Y.
Alternatively, one can describe the dot product as the length of the geometric projection of X onto the unit vector Y when the tails of the two vectors are placed at the same point.