PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 6.3, Problem 117E

(a)

To determine

The geometric descriptions of a vector addition

(a)

Expert Solution
Check Mark

Answer to Problem 117E

let u=(u1,u2)

and v=(v1,v2)

be vectors. Then the sum of u and v is the vector

  u+v=(u1+v1,u2+v2)

Explanation of Solution

Concept used: let u=(u1,u2)

and v=(v1,v2)

be vectors. Then the sum of u and v is the vector

  u+v=(u1+v1,u2+v2)

Calculation:

To add two vectors geometrically position them so that the initial point of one coincides with the terminal points of the other

The sum u+v is formed by joining the initial point of the second vector v with the terminal point of the first vector u . as shown in figure

This technique is called the parallelogram law for vector addition because the vector u+v , often called the resultant of vector addition, is the diagonal of a parallelogram having u and v as its adjacent sides

(b)

To determine

The geometric descriptions of a vector scalar multipication

(b)

Expert Solution
Check Mark

Answer to Problem 117E

  u=(u1,u2) and let k be a scalar then the scalar multiple of k times u is the vector

  ku=k(u1,u2)ku=(ku1,ku2)

Explanation of Solution

Concept used: let u=(u1,u2)

and let k be a scalar then the scalar multiple of k times u is the vector

  ku=k(u1,u2)ku=(ku1,ku2)

Calculation:

The product of a vector v and a scalar k is the vector that is | k | times as long v . if k is positive, kv has the same direction as v , and if k is negative, kv has the direction opposite that of v

As shown in the figure

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 6.3, Problem 117E

Chapter 6 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Prob. 13ECh. 6.1 - Prob. 14ECh. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - 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Publisher:W. H. Freeman
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ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
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Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Vector Addition and Scalar Multiplication, Example 1; Author: patrickJMT;https://www.youtube.com/watch?v=pNMrYACjHXQ;License: Standard YouTube License, CC-BY