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PHCC 141: Physics for Scientists and Engineers I  Fall 2007
1b. Vectors
Due at 11:59pm on Monday, August 27, 2007
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Number of answer attempts per question is:
10
You gain credit for:
correctly answering a question in a Part, or correctly answering a question in a Hint.
You lose credit for:
exhausting all attempts or requesting the answer to a question in a Part or Hint, or incorrectly answering a question in a Part.
Late submissions:
reduce your score by 14.3% over each day late.
Hints
are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions. There is
no penalty
for leaving questions in Hints unanswered.
Grading of
Incorrect Answers
For
MultipleChoice
or
True/False
questions, you lose
100%
/
(
# of options  1
)
credit per incorrect answer.
For
any other
question, you lose 3% credit per incorrect answer.
These problems concern vector addition and subtraction
Vector Addition in a Unit Cell
In nature, substances often possess a crystalline structure. The basic component of a crystal is the unit cell, such as the
rectangular parallelpiped illustrated in the figure . (For the purposes of this problem, take
,
, and
to be positive.)
Find the following quantities. When the question asks for a vector, express your answer as an
ordered triplet. That is, a vector with length
in the
x
direction, length
in the
y
direction,
and length
in the
z
direction should be written as
.
Part A
What is the vector
from point O to point E?
ANSWER:
=
Part B
What is the vector
from point O to point F?
ANSWER:
=
Part C
What is the vector
from point O to point C?
ANSWER:
=
Part D
Hint D.1
How to use the components
Add the components separately.
ANSWER:
=
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Part E
Hint E.1
The meaning of 

Hint not displayed
Hint E.2
Length of a vector
A vector whose
x
,
y
, and
z
components are, respectively,
,
, and
has a length equal to
.
ANSWER:

 =
Part F
Hint F.1
Consider geometry
Hint not displayed
ANSWER:

 =
Part G
ANSWER:

 =
This is a long problem designed to show the maxim: Think geometrically, manipulate with components.
Geometric vs Componentwise Vector Addition
Learning Goal:
To understand that adding vectors by using geometry and by using components gives the same result, and that
manipulating vectors with components is much easier.
Vectors may be manipulated either geometrically or using components. In this problem we consider the addition of two vectors
using both of these two methods.
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 Fall '08
 TOKI
 Physics, Pythagorean Theorem, Dot Product, Assignment Print View, vector cross product

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