Math 1316
Professor Merrill
Name____________________________
Lab 4
1.
Given the vectors AB and CD , find the components of each vector. Let
u  AB and v  CD
2.
a.
A line has direction vector (2,3). What is the slope?_____________
b.
A line has direction vector (4.6). What is the slope?_____________
3.
Find the value of a if the vectors 2,5 and 1, a are
a. parallel
b. perpendicular
4.
All of the following represent vectors except:
a. a car heading southeast at 80mph
c. a storm traveling west at 25kph
b. a barge traveling at 30 knots on a
heading of 20o west of south
d. a person running on a marathon
at 7mph
5.
Draw any vector u. Draw any vector v. Now draw 2u + 3v. Be precise!
6.
Given A(4, 2) and B(0, -1). Give the component form of AB and find AB
Let u = (3, 1), v = (-8, 4) and w = (-6, -2). Find
7.
a. u + v
b. u – v
c. 3u + w
8. Given that u = (8, 45o) and v = (6, -45o), find u  v
d. u +
1
w
2
9. An airplane has a velocity of 500mph in a southwest direction. A 40mph wind is
blowing from the west. Find the resultant speed and direction of the plane. Draw a
picture.
10. Riley is swimming on a course of 040o for 4 miles. He realizes how far he is from
land and turns to a new heading of 100o and swims for 7 miles. How far is he from his
starting point? Draw a picture.
11. Find the component form of the vector, convert it to polar form (show work), find
the magnitude. Circle answers
Find the sum, difference, or product for the complex numbers. Circle your answer. For
the difference, subtract the second number from the first.
12.
14.
11 – 2i and 3 – 4i
sum:
13.
7 + 7i and 1 – i
sum:
difference:
difference:
product:
product:
27 – 13i and 12 + 22i
sum:
15.
10 + 2i and 10 sum:
difference:
difference:
product:
product:
2i
Use the complex conjugate to find the quotient of the two complex numbers. Put
answers in the form a + bi
16.
3  3i
6  6i
17.
2  7i
1 i
18. Change the polar coordinates (5.1, 6o) to rectangular coordinates.
Set your calculator into radians & polar mode. Type in the following equations.
Sketch the graph & answer the questions. Use  in [0, 2].
r=a
19.
r = a
23.
r=3
20.
21.
What shape is graphed?
22.
What is the radius?
r=5
(In window: [0, 4], adjust x & y appropriately to see entire graph)
r = .5
24.
r = 2
25.
What shape to you see?
26.
What does the value of a do to the graph?
r = a sin b 
27.
r = 2sin
28.
r = 3sin2
29.
r = 5cos4
30.
r = 3cos3
31.
What number determines the number of petals? Explain.
32.
Which number determines the length of each petal?
r = a + b sin 
33.
r = 5 + 4cos
34.
r = 1 + 3cos
35. The legs of an isosceles triangle are each 21 cm long and the angle between them
has a measure of 52. What is the length of the 3rd side?
36. Find the area of triangle XYZ if x = 16, y = 25, and <Z = 52.
37. Find the angle between vectors U and V if U = (2,3) and V = (-3,2)