MATH 200 Lecture 2: Lecture Notes Week 2

• School: Drexel University
• Department: Mathematics
• Course: MATH 200
• Professor: unknown

Document Summary

Referred as the inner product in mainly physics classes. ^^^vectors of size n dimensions can be represented by a matrix of 1xn. Notation of vector a dotted with vector b= (cid:1853) (cid:1854) [(cid:1853) (cid:2869),(cid:1853) (cid:2870)(cid:1853) (cid:3041)] [(cid:1854) (cid:2869),(cid:1854) (cid:2870)(cid:1854) (cid:3041)]=(cid:1853) (cid:2869)(cid:1854) (cid:2869)+(cid:1853) (cid:2870)(cid:1854) (cid:2870)++(cid:1853) (cid:3041)(cid:1854) (cid:3041) Ex. (cid:1858) (cid:1853) (cid:1861)(cid:1871) (cid:1872) (cid:1857) (cid:1874)(cid:1857)(cid:1855)(cid:1872)(cid:1867)(cid:1870)[(cid:1853) (cid:2869),(cid:1853) (cid:2870)(cid:1853) (cid:3041)] (cid:1857)(cid:1866)[(cid:1853) (cid:2869),(cid:1853) (cid:2870)(cid:1853) (cid:3041)] [(cid:1853) (cid:2869),(cid:1853) (cid:2870)(cid:1853) (cid:3041)]=||(cid:1853)|| = (cid:1853) (cid:1853) or. Theorem: if u and v are non-0 vectors and is the angle between them, then (cid:1855)(cid:1867)(cid:1871)(cid:4666)(cid:4667)= (cid:3048) (cid:3049) ***two vectors are orthogonal/perpendicular if their dot product. If u and v are non-zero vectors with the same initial point, we equals 0. = the angle between v and the k axis. (cid:2009) is the angle between v and the i axis. (cid:2010) is the angle between v and the j axis. (cid:1855)(cid:1867)(cid:1871)(cid:4666)(cid:2009)(cid:4667) (cid:1853)(cid:1866)(cid:1856) (cid:1855)(cid:1867)(cid:1871)(cid:4666)(cid:2010)(cid:4667) are the direction cosines of v. (cid:1855)(cid:1867)(cid:1871)(cid:4666) (cid:4667) is the direction cosine of v.