University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

58

Pages:

1
Author:

Jasmine Esparza

Workshop #4 1. Which of the following expression are meaningless (i.e. not defined)? For those that are meaningful (i.e. defined), state whether the expression is a scalar or a vector. ~ (a) |~v| × w (b) (|~v|~v) × ~v ~)×w ~ (c) (~v · w ~ (d) (~v × ~v) × w ~ = h−1, −1, 4i. Find three vectors that are perpen2. We have two vectors in R3 , ~v = h1, 3, 2i and w ~ . How many unit vectors are there that are perpendicular to both ~v and w ~? dicular to both ~v and w Find all such unit vectors. ~ = 2(~v × w ~ ). Also verify the ~ = hw1 , w2 , w3 i. Verify the property (2~v) × w 3. Set ~v = hv1 , v2 , v3 i and w ~ = 2(~v · w ~ ). Work from left to right for verifications. (These are examples of the property (2~v) · w ~ = c(~v × w ~ ) and (c~v) · w ~ = c(~v · w ~ ), where c is a scalar. These properties general properties (c~v) × w allow us to simplify computations.) ~ = h−1, −1, 4i, and let θ be the angle between these two vectors. 4. Set ~v = h1, 3, 2i and w (a) Find an expression for cos θ and also for sin θ. (b) What is the quickest way to determine if these two vectors are perpendicular? (c) What is the quickest way to determine if these two vectors are parallel?