Mrs. DiBartolo
Pre-Calculus H
WHRHS
Name ________________________________________________ Date ____________
Unit 14: Vectors Problem Set
In 1 – 6: Find the component form and the magnitude of the vector V.
1.
2.
3.
y
y
y
(3, 4)
(–1, 3)
(2, 1)
x
x
x
(–4, –2)
4.
5.
y
6.
y
(3, 4)
y
(2, 3)
x
x
x
(–1, –2)
(2, –2)
(–4, –2)
(3, –2)
In 7 – 11: Sketch V and find its component form. (Assume that all angles are
measured counterclockwise from the x-axis to the vector.)
7. V is a horizontal vector, pointing toward the right, of length 3.
8. V is a vector of magnitude
5
making an angle of 45° with the positive x-axis.
2
9. V is a vector of magnitude 3 2 making an angle of 150° with the positive x-axis.
10. V is the sum of the vectors: V1 = 2i + j and V2 = 3i + 5j.
11. V is -5W, where W = -i + 3j.
Mrs. DiBartolo
Pre-Calculus H
WHRHS
In 12 – 15: Find the component form of V, and illustrate the indicated vector operations
geometrically, where U = 2i – j and W = i + 2j.
12. V =
14. V = U + 2W
3
U
2
15. V = -U + W
13. V = U + W
In 16 – 18: Find a unit vector in the direction of the given vector.
16. V = 4i – 3j
17. V = i + j
18. V = 2j
In 19 – 21: Find the dot product of these vectors.
19. V = 2i + 4j
U = i – 5j
20. V = -i
U = 2i + 3j
21. V = 2i – j
U = -2i + j
In 22 – 24: Find the angle, in radians, between the vectors.
22. V = i + j
U = 2(i – j)
23. V = 2i + 3j
U = i + 2j
π⎞
⎛
⎛ π⎞
24. V = i ⎜ cos ⎟ + j ⎜ sin ⎟
6⎠
6⎠
⎝
⎝
3π ⎞
⎛
⎛ 3π ⎞
U = i ⎜ cos
⎟ + j ⎜ sin
⎟
4 ⎠
4 ⎠
⎝
⎝
In 25 – 27: Determine whether these vectors are normal, parallel, or neither.
25. V = i – 3j
U = 3i – j
2
1
26. V = − i + j
3
3
U = 2i – 4j
27. V = 4i + 3j
U=
1
2
i- j
2
3
28. Find a unit vector normal to V = 2i + 2j
29. Find a unit vector normal to V = i – 3j
30. Find a unit vector parallel to V = 2i + 2j