Mathematics 1229A/B Study Guide - Midterm Guide: Hyperplane, Book Of Ezekiel, Parallelepiped

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: hi

Document Summary

Use the following for questions 1, 2 and 3. Let u = (1, 0, 2) and v = (0, 1, 3). E: 0 u v = (1, 0, 2) (0, 1, 3) = 1(0) + 0(1) + ( 2)(3) = 0 + 0 + ( 6) = 6. 4. u v = (1, 0, 2) (0, 1, 3) = (0(3) 1( 2), ( 2)(0) 1(3), 1(1) 0(0)) = (0 + 2, 0 3, 1 0) = (2, 3, 1) Find the magnitude (length) of u = 4i 3j. Find all values of c such that the vector u = (c, 1, c, 0) is a unit vector. Solution: in order for u to be a unit vector, it must be true that kuk = 1. We see that kuk = k(c, 1, c, 0)k = pc2 + 12 + ( c)2 + 02 = pc2 + 1 + c2 + 0 = p2c2 + 1.