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

2024
Views:

123

Pages:

2
Author:

kundgetanufv

Workshop #27 1. Set ~r(t) = hcos(t), sin(t)i. (a) Sketch a graph of ~r(t) in R2 . If a particle is moving along this path, in what direction is it moving? π (b) On your graph, sketch ~r . (Don’t forget how the derivative should be graphed! ) π π 4 (c) Compute ~r ·~r 0 . What does this tell you about the relationship between these vectors? 4 4 (Note that this is not always the case for a general curve, this curve is special.) 2. Sketch three different representations of the vector. (Each answer should look like a picture with three vectors starting at different initial points.) (a) ~v = 4~i − 2~j ~ = h1, 2, 3i (b) w 3. Sketch a few of the vectors given by the vector function and determine which vector field matches the function. ~ (a) F(x, y) = ~i + y~j ~ (b) F(x, y) = x~i + y~j ~ (c) F(x, y) = −y~i + x~j 4. Sketch a few of the vectors given by the vector function and determine which vector field matches the function. ~ (a) F(x, y, z) = ~i + y~j + z~k 1 ~ (b) F(x, y, z) = ~i + 2~j + z~k x ~ (c) F(x, y, z) = 7~j