1 EXAM Math 232 July 20, 2007 Name 1. Are the lines defined by x=2+t x=1- s y=3-t and y=3-4s z=1+3t z=-2- s parallel? Perpendicular? Do they intersect?
2. Write the equation of the plane which contains the three points (3, 1, 0), (2, 0, 0) and (4, 2, 1).
- - - 3. Let = 1, 0, -3 , b = 3, -1, 2 and = -2, 3, -2 . Find: a c - - - (a) + 2 - b a c
- - (b) b a
- (c) The vector of magnitude 4 that points in the same direction as b .
4. A constant force of 60, -30 pounds moves an object in a straight line from the point (0, 0) to the point (10, -10). Compute the amount of work done.
5. A person is paddling a kayak in a river with a current of 1 ft/s. The kayak's speed in still water would be 4 ft/s. Find the vector which describes the direction the kayaker should take in order to proceed straight across the river. What is the kayak's actual speed?
6. Find the intersection of the 2x planes - y - z = 4 and 3x - 2y + z = 0.
7. Write the equation of the plane which contains the points (1, 0, -1), (-1, 2, 3) and (2, 1, 1). Now determine whether the plane you just found is perpendicular to the plane 7 = 2x-3y +z
- 8. Find all values of t for which (t) = r t2 + 1, cos (t), e-3t - find (t). r
is a continuous function. Now
9. Find
t1
lim
t+1 t - 1, t2 + 3, t-1
if the limit exists. If it does not exist explain why not.
2
10. Find
0
4 , et-2 , tet t+1
dt
11. Suppose a projectile is launched from a point 12 ft ...