'Introduction To Vectors' Algebra Worksheet

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Vector Worksheet #1
Use separate paper--graph paper if necessary.
Introduction to Vectors
Algebra II/Trigonometry Honors
In Problems 1-6, use the vectors in the figure at the right to graph the following vectors.
v
1. v + w
2. u + v
3. 3u
w
4. w – v
5. 3v + u – 2v
6. 2u – 3v + w
u
In Problems 7- 12, determine whether each statement is true or false.
7. a + b = f
8. k + g = f
9. c + h = k
b
c
f
a
k
10. b + k + g = a
11. a – b = g – k
12. a + b + k + g = 0
g
h
In Problems 13 – 18, if vector v has initial point P and terminal point Q, write v in the form
ai + bj and in the form
a,
b
. That is, find its position vector.
13. P(3,2), Q(8,9)
14. P(5,3), Q(1,0)
15. P(-1, -5), Q(6,2)
16. P(4,7), Q(-4,-2)
17. P(-1,4), Q(6, -5) 18. P(-3,-5), Q(-5,-7)
In Problems 19 – 22, find 2u, u + v, and 3u – 4v, for the given vectors of u and v.
19. u =
2
7 ,
, v =
3
1 ,
20. u =
2
5 ,
, v =
2
8 ,
21. u = i, v = – 2j
22. u = 2i, v = 3i – 2j
In Problems 23 – 28, find v .
23. v = 3i – 4j
24. v = -5i + 12j
25. v = i – j
26. v = -i – j
27. v = -2i + 3j
28. v = 6i + 2j
Answers:
1)
2)
3)
4)
5)
6)
7) T 8) F 9) T 10) F 11) T 12) T
13)<5,7>; 5i+7j
14) <-4,-3>; -4i-3j 15) <7,7>; 7i+7j 16) <-8, -9>; -8i-9j
17) <7,-9>; 7i-9j 18) <-2,-2>; -2i-2j
19) <4,14>; <5,8>; <-6,17>
20) <-4,10>; <0,13>; <-14,-17> 21) <2,0>; <1,-2>; <3,8>
22) <4,0>, <5,-2>, <-6,8>
23) 5 24) 13 25)
26)
27)
28)
2
2
13
2
10

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