For instance , in three-dimensional space , the dot product of vectors ( 1 , 3 , − 5 ) and ( 4 , − 2 , − 1 ) is : In Euclidean space , a Euclidean vector is a geometrical object that possesses both a magnitude and a direction .
The same way , in a dimension 3 , the dot product of vectors ( a , b , c ) and ( d , e , f ) is ad + be + cf. For example , the dot product of two three-dimensional vectors ( 1 , 3 , − 5 ) and ( 4 , − 2 , − 1 ) is In Euclidean geometry , the dot product , length , and angle are related .