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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Chapter 10.2, Problem 43E
To determine

ToFind:The angle θ between the vectors u=10i+40j and v=−3j+8k

Expert Solution & Answer
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Answer to Problem 43E

Theangle between the given vectors is approximately θ≈1.91

Explanation of Solution

Given:

The vectors u=10i+40j and v=−3j+8k

Concept Used:

If θ is the angle between two nonzero vectors u and v , then

  cos(θ)=u·v‖u‖‖v‖

Calculation:

Given the vectors u=10i+40j and v=−3j+8k

That is

  u=10i+40j+0k=〈10,40,0〉

And

  v=0i−3j+8k=〈0,−3,8〉

For and angle θ between two nonzero vectors u and v , we have cos(θ)=u·v‖u‖‖v‖

Substituting the values of u and v

  cos(θ)=〈10,40,0〉·〈0,−3,8〉‖〈10,40,0〉‖‖〈0,−3,8〉‖=(10)(0)+(40)(−3)+(0)(8)((10)2+(40)2+02)(02+(−3)2+(8)2)=0−120+0(100+1600+0)(0+9+64)

  =0−120+0(100+1600+0)(0+9+64)=−120(1700)(73)=−120101773=−121773

That is

  θ=cos−1(−121773)≈1.91

Therefore, θ≈1.91

Conclusion:

Theangle between the given vectors is approximately θ≈1.91

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Chapter 10.2, Problem 42E
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Chapter 10.2, Problem 44E

Chapter 10 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Prob. 63ECh. 10.4 - 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