For the given vectors v and w find: (a) v+w (b) w -v w

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 71E
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Adding vectors geometrically:
Vectors (Geometric vectors):
We position the vectors v and w so that the terminal point of v coincides with the initial point of
w.
In this part we want to explain what the vector is, how we graph the vector and how we do basic
operations with the vectors if we have their graphs.
The vector v +w is then the unique vector whose initial point coincides with the initial point of v
and whose terminal point coincides with the terminal point of vector w.
A vector is a quantity that has both magnitude and direction.
Terminal point of w
V + w
W.
Terminal
point
Initial
point
Initial point of v
(a) Line containing Pand Q
(b) Line segment PO
(c) Directed line segment PO
Subtracting vectors geometrically:
In a picture (c) we have geometric vector or directed line segment PQ
Pis called initial point and Q terminal point.
To explain the difference of two vectors we need to explain what the opposite vectors are.
Opposite vectors are vectors with the same magnitude but opposite direction.
If a vector v has the same magnitude and the same direction as directed line segment PQ, we
write: v = PO
If v is vector - vis its opposite vector.
S.
The difference of two vectors v- w is defined by:
v-w =v+(-w)
(We are adding vector v and vector opposite to w)
R
v - W
equal vectors
V - W
Transcribed Image Text:Adding vectors geometrically: Vectors (Geometric vectors): We position the vectors v and w so that the terminal point of v coincides with the initial point of w. In this part we want to explain what the vector is, how we graph the vector and how we do basic operations with the vectors if we have their graphs. The vector v +w is then the unique vector whose initial point coincides with the initial point of v and whose terminal point coincides with the terminal point of vector w. A vector is a quantity that has both magnitude and direction. Terminal point of w V + w W. Terminal point Initial point Initial point of v (a) Line containing Pand Q (b) Line segment PO (c) Directed line segment PO Subtracting vectors geometrically: In a picture (c) we have geometric vector or directed line segment PQ Pis called initial point and Q terminal point. To explain the difference of two vectors we need to explain what the opposite vectors are. Opposite vectors are vectors with the same magnitude but opposite direction. If a vector v has the same magnitude and the same direction as directed line segment PQ, we write: v = PO If v is vector - vis its opposite vector. S. The difference of two vectors v- w is defined by: v-w =v+(-w) (We are adding vector v and vector opposite to w) R v - W equal vectors V - W
Question 1:
|
For the given vectors v and w find:
(a) v+ w
(b) w -v
w
Transcribed Image Text:Question 1: | For the given vectors v and w find: (a) v+ w (b) w -v w
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