MAC 2313 Lecture Notes - Lecture 2: Dot Product, Unit Vector, Trigonometry

• School: University of Florida
• Department: Mathematics
• Course: MAC 2313
• Professor: Jason Kozinski

Document Summary

Several di erent products can be de ned for vectors. In the previous lecture we de ned the product of a scalar with a vector. We now de ne a new product in which one vector is multiplied by a second vector. The dot product of vector u and v, represented symboli- cally as u v, is de ned by u v = where (cid:18) is the angle (0 (cid:18) (cid:25)) between the vectors. Note that the resulting product is a scalar. Two vectors are said to be orthogonal if their dot prod- uct is equal to zero. For nonzero vectors, this implies that the angle between the vectors is. The zero vector is orthogonal to all other vectors. The de nition of the dot product does not provide a conve- nient means of computation for component-wise representa- tions of vectors.