Book review
Vectors in the Plane
- Course
- Institution
Algebra and Trigonometry course
[Show more]
Seller
Follow
Studydesk
Content preview
,Vectors in the Plane, 7.3 Vectors in the Plane
Introduction What you should learn
Represent vectors as directed
Many quantities in geometry and physics, such as area, time, and temperature, can
line segments.
be represented by a single real number. Other quantities, such as force and velocity,
Write the component forms of
involve both magnitude and direction and cannot be completely characterized by a
vectors.
single real number. To represent such a quantity, you can use a directed line segment,
\
Perform basic vector operations
as shown in Figure 7.11. The directed line segment PQ has initial point P and
\
and represent vectors
terminal point Q. Its magnitude, or length, is denoted by PQ and can be found by
graphically.
using the Distance Formula.
Write vectors as linear
Q combinations of unit vectors.
PQ Terminal Find the direction angles of
point vectors.
P
Use vectors to model and solve
Initial
point real-life problems.
Figure 7.11 Figure 7.12 Why you should learn it
Vectors are used to analyze
Two directed line segments that have the same magnitude and direction are
numerous aspects of everyday life.
equivalent. For example, the directed line segments in Figure 7.12 are all equivalent.
Exercise 99 on page 571 shows
The set of all directed line segments that are equivalent to a given directed line segment
\ \
you how vectors can be used to
PQ is a vector v in the plane, written v = PQ . Vectors are denoted by lowercase,
determine the tension in the cables
boldface letters such as u, v, and w.
of two cranes lifting an object.
EXAMPLE 1 Showing That Two Vectors Are Equivalent
Show that u and v in the figure at the right y
(4, 4)
are equivalent. 4 S
Solution v
3
(1, 2) (3, 2)
From the Distance Formula, it follows 2
\ \
that PQ and RS have the same magnitude. R Q
\ 1
u
PQ = √(3 − 0)2 + (2 − 0)2 = √13 (0, 0)
x
\
RS = √(4 − 1) + (4 − 2) = √13
2 2 P 1 2 3 4
Moreover, both line segments have the same direction, because they are both directed
toward the upper right on lines having the same slope.
\ 2−0 2
Slope of PQ = =
3−0 3
\ 4−2 2
Slope of RS = =
4−1 3
\ \
Because PQ and RS have the same magnitude and direction, u and v are equivalent.
Show that u and v in the figure at the right y
are equivalent.
4
(5, 3)
3
(2, 2) v S
2 R
(3, 1)
1 u Q
x
P 1 2 3 4 5
(0, 0)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Studydesk. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
59804 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now