Math 241 - Exam #1 Solutions

1a. a + 3b = 3i + 2j - 2k
1b. |b| = sqrt(5)
1c. |a . (c-b) | = 7
1d. comp_c(b) = -1/sqrt(2)
1e. b x c = 2i + j + 2k
1f. c . (a x b) = 4

2a. PQ = <-2,-2,-8>
2b. x = 1 - 2t, y = 2 - 2t, z = 3 - 8t
2c. (x-1)/(-2) = (y-2)/(-2) = (z-3)/(-8)

3. Look at only the vertical forces
30 sin 62 + 20 sin 45 = 9.8 m
m = 4.14 kg

4. n = <3,3,1>, point (t=0) = (0,1,4)
3x + 3y + z = 3(0) + 3(1) + (4) = 7

5. Area = 1/2 | a x b |, a = PQ, b = PR
Area = 1/2 | <1,4,6> x <2,1,8> | = 13.61

6. Domain = {y^2-x^2>0} or {|y|>|x|}. Hourglass shape.
f(3,5) = 2

7. Cylinder of radius 2 from z = -2 to z = 2, with a hole of radius 1, drilled along the z-axis. Like a thick-walled pipe.

ccollins@math.utk.edu
Last Modified: Feb. 4, 1999