Vector Dot Product Learning Goal: To understand the rules for

Cheexorgeny 2021-12-16 Answered
Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors A=(2,1,4),B=(3,0,1)
Angle between the vectors A and B What is the angle θAB between A and B? Express your answer numerically to three significant figures in radians. θAB= radians
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Expert Answer

Shannon Hodgkinson
Answered 2021-12-17 Author has 34 answers
AB=|A||B|cos(θ)
cos(θ)=AB|A||B| We have AB=10
|A|=22+12+(4)2
|A|=4+1+16
|A|=21
|B|=(3)2+02+12
|B|=9+0+1
|B|=10
cos(θ)=102110
cos(θ)=1021=0.69006
θ=cos1=0.69006
θ=2.33 radians.
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Paineow
Answered 2021-12-18 Author has 30 answers
The magnitude of vector A is,
A=Ax2+Ay2+Az2
Substitute 2 for Ax, 1 for Ay and -4 for Az, The magnitude is,
A=(2)2+(1)2+(4)2
=4.58
The magnitude of vector B is
B=Bx2+By2+Bz2 Substitute -3 for Bx, 0 for By and 1 for Bz, The magnitude is, A=(3)2+(0)2+(1)2
=3.16
The angle between vectors is,
θAB=cos1(AB|A||B|)
θAB=cos1(10(4.58)(3.16))
=134
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nick1337
Answered 2021-12-28 Author has 510 answers

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