MATH 240 Lecture Notes - Lecture 8: Dot Product, Unit Vector, Cross Product

• School: University of Maryland
• Department: Mathematics
• Course: MATH 240
• Professor: Raluca Rosca

Document Summary

Recall that a unit vector is any vector with a magnitude of 1. Given a nonzero vector (cid:2204), then vector (cid:2203) will be a unit vector if u= (cid:2869)||(cid:2204)||(cid:2204: find a unit vector that points in the same direction of (cid:2204)=(cid:4666)(cid:886),(cid:888),(cid:887)(cid:4667). All we do is take the magnitude of (cid:2204). Easy, we take the magnitude and see if it is equal to 1. So indeed, u is the unit vector: find the unit vector going in the opposite direction. For this, all we do is pop a negative sign on the front of the vector. Given two vectors and the angle between them, we can calculate the dot product of two vectors. calculated as follows. If u and v are vectors and the angle between them is , then their dot product is: calculate the dot product of (cid:2203)=(cid:4666)(cid:884),(cid:886),(cid:885)(cid:4667) and (cid:2204)=(cid:4666)(cid:885),(cid:887),(cid:886)(cid:4667) if the angle between them is (cid:2203) (cid:2204)=||(cid:2203)|| ||(cid:2204)||cos (cid:4666)(cid:4667) Ok, first we have to find our two magnitudes.