Homework Assignment
Solutions
Section 5.1
y
5.1.1. True or False: ~u − ~v = ~v − ~u for all vectors ~u and ~v .
Answer: False
~u − ~v
5.1.2. True or False: 3~v + ~v = 4~v for all vectors ~v .
Answer: True
~u
x
5.1.3. Consider the vectors below:
~u + ~v
~v
−3~u
~u
~v
5.1.5. Vectors ~u, ~v , and w
~ are shown below. Sketch ~u +~v + w.
~
y
~u
Of the following vectors, which one is not drawn? This
is a multiple choice question; there is only one correct
answer.
x
(a) −2~u
(b) −~v
w
~
(c) ~u + ~v
~v
(d) ~u − ~v
(e) ~v − ~u.
Answer: On graph:
Answer: (d) ~u − ~v
y
5.1.4. The vectors ~u and ~v are drawn below. Sketch ~u + ~v ,
~u − ~v , and −3~u. Be sure to label your answers.
~u
y
x
~u + ~v + w
~
w
~
~u
x
~v
Answer: On graph:
~v
5.1.6. Suppose that k~v k = 5 and kwk
~ = 12. Suppose also
that, when drawn starting at the same point, ~v and w
~
make an angle of π4 .
(a) Find kw
~ + ~v k and round to two decimal places.
Answer: 15.93
(b) Find kw
~ − ~v k and round to two decimal places.
Answer: 9.17
5.1.7. The vector ~v represents the displacement vector from
Portland, Oregon to Houston, Texas. The vector
w
~ represents the displacement vector from Houston,
Texas to Akron, Ohio. Use the vectors ~v and w
~ to
answer the following questions:
Last Updated: March 29, 2014
Page 1 of 2
Homework Assignment
Solutions
Section 5.1
(a) What is the displacement vector of a plane which
flies from Akron, Ohio to Houston, Texas?
Answer: −w
~
f~
(b) In order to fly home from Portland to Akron I
have a layover in Houston. Find a vector which
describes my total displacement over the whole
trip.
Answer: ~v + w
~
(c) It is approximately 3000 km from Portland to
Houston. It is approximately 5500 km from Anchorage, Alaska to Houston. A plane flies in
a straight line from Houston to Anchorage and
during the flight it passes directly over Portland.
Find a vector which describes the displacement of
the plane.
v
Answer: − 11
6 ~
2π
3
~g
Answer: The magnitude of the resultant force is 35 N.
The force is drawn below.
f~
5.1.8. The forces f~ and ~g are acting on an object with
kf~k = 40 N and k~g k = 25 N as shown below. Draw
the resultant force and find its magnitude. Round to
two decimal places.
resultant
~g
Last Updated: March 29, 2014
Page 2 of 2