'Vectors' Algebra Worksheet
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1Vector Worksheet #2
Use separate paper or graph paper if necessary.
Algebra II/Trig Honors
Vectors - Worksheet 2
=
−
−
=
5 −
=
−
=
, 3 −
a
1 ,
4 ,
b
, 6
, 4
1
u
3
4 ,
v
2
Given the vectors
,
,
, and
, find each of the
following linear combinations.
1
3
1. 3 u − 4 v
2. −4 u + 5 v
u +
3.
v
2
2
−2
2
1
4
4. 2 a + 7 b
a +
a −
5.
b
6.
b
3
2
5
5
u • v
θ
=
to find the angle θ between the vectors u and v .
Use the formula cos
u v
=
−
=
−
v
6
9 ,
=
=
, 3 −
v
6
4 ,
u
3
5 ,
u
2
7.
8.
=
=
=
, 7 −
=
−
, 1 −
u
2
4 ,
6 ,
u
2
1 ,
v
4
v
4
2 ,
9.
10.
;
=
−
u
2
0 ,
3 ,
=
=
, 1 −
=
−
−
v
2
2 ,
2 ,
u
2
3 ,
v
, 2
, 1
2
11.
;
12.
;
Resolve each vector into component form.
13. 40 lbs at 40 °
14. 60 lbs. at 100 °
15. 6N at 220 °
16. 12N at 300 °
Find the magnitude and direction (as an angle in standard position) of each vector in Problems
17-22
17. <3,-4>
18. <-5,10>
19. <-6,-2>
20.
21. <-1,7>
22. <14,8>
, 3 −
1
−
−
−
1 −
14
14
4
4
13
° 2
87
.
1. <-21,20> 2. < 27,-26> 3. <3,-1> 4. <32,-26,1> 5. <
> 6. <
> 7.
8.
,
,
,
,
3
3
6
5
5
5
° 4
° 3
° 1
° 8
157
.
56
.
100
.
80
.
°
9.
10.
11.
12. 100.26
13. 30.6i + 25.7j 14. –10.4i + 59.1j
ϑ
ϑ
=
−
°
=
°
53
1 .
5
5
116
6 .
15. –4.6i + -3.9j 16.6i – 10.4j
17. m= 5,
18. m=
,
ϑ
ϑ
ϑ
ϑ
=
°
= 30
−
°
=
°
=
°
2
10
198
4 .
5
2
98
1 .
2
65
29
7 .
19. m=
,
20. m=2,
21. m=
,
22. m=
,
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