Lesson Two
Assignment
Name:
r
r
r
In 1-4,
r let
r u = (0, -5), v = (2, 3), and w = (-1, -6). Find the sum or difference.
1. ur+ v
2. -rw r
3. vr - w
r
 v - ur + w

4.
 
r
r

In 5 and 6, let s = [3, 15º] and t = [2, 160º]. Compute and express the answer in its polar
  representation.
  r rt
5. sr +
6. - s


r r
r
r
7. If u + v is the zero vector, prove that v is the opposite of u .


r
r

8. Show that v = (2 cos 215º, 2 sin 215º) is the opposite of u = (2 cos 35º, 2 sin 35º).
 

9. Two people push a disabled 
car with the forces shown
at the right.


15º
2,000 lb
2,500 lb
30º
a. Give the resultant force in polar form.
b. Interpret your answer to part a.
c. How much more forward force (to the right) is provided by the person exerting 2,500
lb of force than the person exerting 2,000 lb of force?
10. Relative to the water, a boat is moving with a speed of 20 mph in the direction 15º
west of north. Due to the current which is moving in the direction 60º south of east, the
boat is actually heading north relative to the land.
a. Find the speed of the current.
b. Find the speed of the boat moving north.
r
r
11. The vector v and w are shown at the right. Sketch the following.

 

 
r
v

r
w


r
r
a. v r+ w
b. -rw r
c. w - v r
r
In 1-4, let u = (6, -2) and v = (-1, 5), and compute.










Lesson Two
Assignment
r
1. 12 u
r
2. 2 v
r
r
3. 12 u + 2 v
r
r
4. 2 u - 3 v
Name:
r
r
5. Show that v = (3, 7) and u = (-18, -42) are parallel.

6. Show that the line passing through (-1, 2) and (3, 4) is parallel to the vector vr = (-2, 1)


r
r
In 7-10,
determine
whether
or
not
and
are parallel.
u
v
r
r

7. u = (2, -3), v = (4, 6)
r
r
1
8. u = (-1, - 2 ), v = (10, 5)
r
r
9. u r= (7, 3), v =r(7, 3)


10. u = [3, 20º], v = [5, 200º]

 vr = (5, 1) and -2 vr on the same set of axes.
Sketch
11.




QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
r
12. a. Give the endpoint of a vector w which has polar representation [2, 150º] and starts
at the point(-1, 1).
r
b. Give the endpoint of the vector 3 w if it starts at (-1, 1).
c. Sketch both vectors.


Lesson Two
Assignment
Name:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
r
r
13. Given the vectors u and v shown at the right. Sketch the following.
r
u

r
v

r
a. 2 ur
b. -3rv r
c. 2 u - 3 v


r

14. a. Find parametric equations of the line through (-3, 5) that is parallel to the vector v
=(3, 3).
 b.Graph the line.

QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.