MATH 2204 Study Guide - Comprehensive Final Exam Guide - Euclidean Vector, Trigonometric Functions, Polar Coordinate System

93 views32 pages

Document Summary

Daniel eisert | math-2204: three-dimensional coordinate systems are divided into octants with the first octant being determined by the positives axes, every coordinate is an ordered triple: (cid:4666)(cid:1853),(cid:1854),(cid:1855)(cid:4667) Types of planes: xy-plane all z-values are equal to zero, yz-plane all x-values are equal to zero, xz-plane all y-values are equal to zero. |(cid:2869)(cid:2870)|= (cid:4666)(cid:1876)(cid:2870) (cid:1876)(cid:2869)(cid:4667)(cid:2870)+(cid:4666)(cid:1877)(cid:2870) (cid:1877)(cid:2869)(cid:4667)(cid:2870)+(cid:4666)(cid:1878)(cid:2870) (cid:1878)(cid:2869)(cid:4667)(cid:2870: change equal sign to a sign for balls three-dimensional spheres. (cid:4666)(cid:1876) (cid:4667)(cid:2870)+(cid:4666)(cid:1877) (cid:1863)(cid:4667)(cid:2870)+(cid:4666)(cid:1878) (cid:1864)(cid:4667)(cid:2870)=(cid:2870) Length of a three-dimentional vector: components |(cid:2183)|= (cid:2869)(cid:2870)+(cid:2870)(cid:2870)+(cid:2871)(cid:2870: (cid:2183)+(cid:4666)(cid:2184)+(cid:2185)(cid:4667)=(cid:4666)(cid:2183)+(cid:2184)(cid:4667)+(cid:2185, (cid:2183)+(cid:2184)=(cid:2184)+(cid:2183, (cid:2183)+(cid:4666) (cid:2183)(cid:4667), (cid:2183)+=(cid:2183, (cid:4666)(cid:1855)+(cid:1856)(cid:4667)(cid:2183)=(cid:1855)(cid:2183)+(cid:1856)(cid:2183, (cid:1855)(cid:4666)(cid:2183)+(cid:2184)(cid:4667)=(cid:1855)(cid:2183)+(cid:1855)(cid:2184, (cid:4666)(cid:1855)(cid:1856)(cid:4667)(cid:2183)=(cid:1855)(cid:4666)(cid:1856)(cid:2183)(cid:4667, (cid:883)(cid:2183)=(cid:2183) (cid:2193)= (cid:2191)= (cid:2192)= Standard basis vectors: all have lengths of one. Daniel eisert | math-2204: two nonzero vectors are perpendicular or orthogonal if the angle between them is. Properties: used when multiplying two vectors, multiply corresponding components, if theta is the angle between vectors a and b, then: (cid:2183) (cid:2184)=(cid:1853)(cid:2869)(cid:1854)(cid:2869)+(cid:1853)(cid:2870)(cid:1854)(cid:2870)+(cid:1853)(cid:2871)(cid:1854)(cid:2871) (cid:2183) (cid:2184)=|(cid:2183)||(cid:2184)| .

Get access

Grade+20% off
$8 USD/m$10 USD/m
Billed $96 USD annually
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
40 Verified Answers

Related textbook solutions