Mathematics 1229A/B Lecture Notes - Lecture 4: Parallelepiped

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

Document Summary

Math 1229 lecture 4 dot & cross product continued. Theorem: for vectors u, v, and w in r3 (u x v) w = 0 if and only if u, v, and w are coplanar, that is, lie in the same plane. Theorem: the volume of a parallelepiped is |(u x v) w| absolute value. Example 1: find the volume of the parallelepiped determined by u = (4,-2,1), v = (3,-1,2), and w = (-1,1,-1). U x v = (-2)(2) (-1)(1), (1)(3) (2)(4), (4)(-1) (3)(-2) U x v = (-4) (-1), 3 8, (-4) (-6) U x v = (-3, -5, 2) w. U x v w = (-3,-5,2) (-1,1,-1) U x v w = (-3)(-1) + (-5)(1) + (2)(-1) U x v w = 3 + (-5) + (-2) U x v w = |(-4)| absolute value. U x v w = 4 final answer.