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

2024
Views:

95

Pages:

1
Author:

laqala0uk

Workshop #3 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. 1 ~ w |~v| 1 (b) |~v| ~ w ~ (c) ~v · w (a) ~ (d) |~v| · w (e) (|~v| + 4)~ w ~ = h1, 5i. 2. We have two vectors in R2 , ~v = h9, 3i and w (a) Carefully sketch these vectors. Find an expression for cos θ, where θ is the angle between ~v and ~. w ~ onto ~v? Sketch where it is on your picture. (b) On your picture, where is the projection of w (c) Find a unit vector in the direction of this projection. What is this unit vector also parallel to? (d) Using trigonometry, what is the length of this projection? (e) Any vector can be expressed as a scalar multiplication: (length of vector) · (unit vector in the direction of that vector). Use this, and your work above, to find the vector that represents the projection of w ~ onto ~v . ~ = h−4, 2, 1i. Use only the dot product in this 3. We have two vectors in R3 , ~v = h1, 3, 2i and w problem. (a) Prove or disprove: ~v⊥~ w. (b) There is a long way and a short way to do part (a), what are they? ~. (c) Prove or disprove: ~v k w