r r
Draw and then label the vector sum A + B .
1.
2.
3.
r
A
r
A
r
A
r
B
r
B
r
B
r r
r r r r
4. Show that vector addition is associative. I.e. show that ( A + B ) + C = A + ( B + C )
r
r
r
5. Show that vector multiplication is distributive. I.e. show that (α + β ) A = α A + β A
r r r
Draw and then label the vector C = A − B .
6.
7.
8.
r
A
r
A
r
A
r
B
r
B
r
B
r
r
1 r
9. The vector A is shown. Draw and label the vectors 3A and A .
2
r
A
10. Is it possible to add a scalar to a vector? If not, explain. If so, then give an example.
r
11. How would you define the (null) vector 0 ?
r
r
r
r
r
12. Given A and B draw and label the vector C = 3 A + 4 B .
r
A
r
B
r
r
r
r
r
13. Given A and B draw and label the vector C = 4 A − 3B .
r
A
r
B
Draw and label the x- and y-components of the vectors shown below
14.
15.
y
16.
y
y
r
A
r
A
x
x
x
r
A
Numerically determine the x- and y-components of the vectors shown below
17.
18.
r
B
y
19.
y
y
4
x
3
60
r
A
30o
x
r
C
2
45o
x
o
Ax = __________
Bx = __________
Cx = __________
Ay = __________
By = __________
Cy = __________
Draw and label the vectors whose components are given below and determine the
magnitude of each.
20. Ax = 3, Ay = 2
y
x
21. Ax = −2, Ay = 4
22. Ax = 2, Ay = −3
y
y
x
x
23. Can a vector have a component that is equal to zero and still have a non-zero
magnitude? Explain.
24. Can a vector have zero magnitude if one of its components is non-zero? Explain.
25. Suppose you have two vectors that have different magnitudes. Can the vector sum
ever be zero? Explain.
26. Redefine the null vector using the idea of components.
Draw and label the following vectors (given in component form).
r
27. A = 3 xˆ + 2 yˆ
r
29. C = 2 xˆ − 3 yˆ
r
28. B = −2 xˆ + 4 yˆ
y
y
x
y
x
x
Write the following in component form
30.
31.
r
B
y
32.
y
y
4
x
3
60
r
A
r
A = __________
30o
x
r
C
2
45o
x
o
r
B = __________
r
C = __________
r r r r
33. What is the resultant vector R = A + B − C of the vectors defined above? Write your
answer in component form.
r r
34. Compute the scalar (dot) product of the vectors S = A • B given above.
r r r
35. Compute the vector (cross) product of the vectors V = A × B given above.