Vector Exam Review
Directions: Show all work on a separate sheet of paper. Use degrees
for all the directions and round all answers to one decimal place.
Vector Quiz
1) Given the following vectors
a) Construct a – 2b, find its magnitude and direction
b) Construct 3b + c - a, find its magnitude and direction
2) Write the ordered pair notation of the vector that points from
C(17, -18) to B(17, -32). Find ||CB|| and its direction.
3) If m = 3j, p = 6i + 4j and q = -6i + 9j find the following
a. p · q, are the vectors orthogonal?
b. Find the angle between m and q.
4) If a = 6i + 2j + 10k and b = 4i + j + 9k, find a x b and show
the resulting vector is orthogonal to a and b.
5) Adding Forces The magnitude and direction exerted by two
tugboats towing a ship are 4200 pounds, 65º east of north, and
3000 pounds, 58º east of south, respectively. Find the
magnitude and direction of the resultant force.
6) Finding Airspeed After 1 hour in the air, an airplane arrives at
a point 200 miles due south of its departure point. If there was
a steady wind of 30 miles per hour from the northwest
(traveling along a bearing of 130°) during the entire flight,
what was the average airspeed of the airplane?
7) Work Find the work done by a force of 4 pounds acting in the
direction of 38° to the horizontal in moving an object 4 feet
from (0, 0) to ( 4, 0).
8) Work A force of 5 pounds acts in the direction of 4° to the
horizontal. The force moves an object along a straight line
from the point (4, 10) to the point (14, 15), with distance
measured in feet. Find the work done by the force. Round the
answer to one decimal place, if necessary.
1)
a)
b)
4.5, 116.6 degrees
2) 14, 270 degrees
3) a) 0, yes b) 33.7 degrees
4) <8, -14, -2>
5) 6353 pounds, 1.7
6) 178 mph
7) 12.6 ft-lb
8) 52 ft-lb
9.1, 6.3 degrees