homework 10 Q

step by step answer 

1. Use the dot product to find the angle between the two vectors, u = [-3,-5] and

v = [-6,1]. Give the exact answer, i.e. leave the answer in an inverse trig function form.

2. Let A = (-1,1), B = (2,1), C = (-3,0) and D = (1,1).

(a) Find the component form and magnitude of AC + BD

(b) Find a unit vector in the direction of AC

3. Convert the polar coordinates to rectangular coordinates

(a)

(3,135)
o

(b)

3
(2,)
4
p

4. Eliminate the parameter and identify the graph:

(a)
4,5804
xtytt
=+=-££

(b)
32cos,42sin
xtyt
=-=+

5. Use DeMoivre’s theorem to simplify the following complex numbers:

(a)
3
[2(cossin)]
66
i
pp
+

(b)
[5(cos123sin123)][3(cos57sin57)]
oooo
ii
++

\

(c)
55
12(cossin)
66
6(cossin)
33
i
i
pp
pp
+
+

6. Find and graph the three cube roots of i.

7. Determine the resultant of two forces: one is of 4 pounds along the x-axis, the

Other is 2 pounds making an angle of
50
o
with the positive x-axis. Give the

Magnitude and direction of the resultant.

8. Find and graph the 4 fourth roots of 3 + 3i

9 Convert the polar equation to rectangular form and identify the graph:

3cos2sin
r
qq
=–

10. An airplane is flying on a bearing of
80
o
, at 540 mph. A wind is blowing with the bearing of
100
o
at 55 mph. Find the actual speed and direction of the airplane.

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