Active Learning: Vectors
rev. 5/12
I Vector Representation (Bold type represents a vector quantity)
1. Answer the following about vectors:
A. Can the magnitude of a vector be considered negative? Explain
B. Can a vector be considered negative? Explain
C. Can one vector be the negative of another vector? Explain
2. Express the following vectors in unit vector notation (i, j, k).
A. The velocity vector V = 24 m/s @ 58° N of E.
B. The force vector F = 120 N @ 32° in the 2nd quadrant?
C. The displacement vector R = 12 m @ 248°
3. What are the magnitude and direction of the following?
A. The displacement vector R = 12i + 15j m
B. The velocity vector V = 18i – 6j m/s
4. Can the magnitude of a vector be less than the magnitude of one of its components? Explain
Active Learning: Vectors
II Vector Addition and Subtraction
1. Perform the following vector additions and subtractions for the following vectors.
A=
→
B=
←
C=
→
D=
←
A. Draw the vector R1 = A + C
B. Draw the vector R2 = A – C
C. Draw the vector R3 = A + D
D. Draw the vector R4 = A - D
2. A person walks a distance due south, then the same distance 30° N of W, then twice that distance 45°
N of E. Where is she?
a. About due S of where she started
b. About 20° N of E from where she started
c. About 45° N of W from where she started
d. About 55° N of E from where she started
3. A person walks 100 m due west, then 200 m due north, then 50 m due east. How far is he from his
starting point?
4. The initial velocity is V1 = -5 j m/s. The final velocity is V2 = +5 i m/s. What is ∆V = V2 – V1?
5. Find the vector sum A -2B + C for the following vectors first graphically and then by components.

A 90 m @ 170

B 50 m @ 65

C 130 m @ 80
Active Learning: Vectors
III Relative Velocity
1. What do we mean by relative velocity?
2. Boat A is traveling with speed 15 m/s. Boat B is traveling with speed 10 m/s?
A. Is there any way the relative speed between the two can be 30 m/s?
B. Is there any way the relative speed between the two can be 0?
C. What are the maximum and minimum relative speeds between the two boats? Draw their velocity
vectors to produce the max and minimum relative speeds.
3. A plane is flying with a velocity over the ground of 180 km/hr in a direction 15° S of W. The plane’s
airspeed is 200 km/hr with a compass heading 40° S of W.
A. Why aren’t the two velocities the same?
B. What is the wind velocity that day?