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warfreak131
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Question
Let vectors [tex]\vec{A} =(2,1,-4), \vec{B}=(-3,0,1), \vec{C}=(-1,-1,2).[/tex]
What is the angle (in radians) [tex]\theta_{AB} [/tex] between [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]?Important equations
[tex]\vec{A} \cdot \vec{B} = \vert \vec{A} \vert \,\vert \vec{B}\vert \cos(\theta)[/tex], where [tex]\theta[/tex] is the angle between [tex]\vec{A}[/tex] and [tex]\vec{B}.[/tex]
My attempt
[tex]\vec{A}\cdot\vec{B} = (2*-3) + (1*0) + (-4*1) = -6 - 4 = -10[/tex]
[tex]|\vec{A}||\vec{B}| = (2*3) + (1*0) + (4*1) = 10[/tex]
therefore, [tex]-10 = 10*cos(\theta)[/tex]
[tex]-1 = cos(\theta)[/tex]
[tex]arccos(-1) = \theta[/tex]
[tex]180 = \theta[/tex]
[tex]180 = \pi[/tex] [tex]radians[/tex]
but it says [tex]\pi[/tex] isn't the right answer
But I don't think that sounds right, because [tex]\vec{A}[/tex] is at [tex]\arctan{\frac{1}{2}}[/tex] (26.7) degrees, and [tex]\vec{B}[/tex] runs along the negative X axis at 180 degrees, So that's a difference of 153.3 degrees. And if you convert that to radians, you get approximately [tex]\frac{17\pi}{20}[/tex] radians, which isn't right either.
Let vectors [tex]\vec{A} =(2,1,-4), \vec{B}=(-3,0,1), \vec{C}=(-1,-1,2).[/tex]
What is the angle (in radians) [tex]\theta_{AB} [/tex] between [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]?Important equations
[tex]\vec{A} \cdot \vec{B} = \vert \vec{A} \vert \,\vert \vec{B}\vert \cos(\theta)[/tex], where [tex]\theta[/tex] is the angle between [tex]\vec{A}[/tex] and [tex]\vec{B}.[/tex]
My attempt
[tex]\vec{A}\cdot\vec{B} = (2*-3) + (1*0) + (-4*1) = -6 - 4 = -10[/tex]
[tex]|\vec{A}||\vec{B}| = (2*3) + (1*0) + (4*1) = 10[/tex]
therefore, [tex]-10 = 10*cos(\theta)[/tex]
[tex]-1 = cos(\theta)[/tex]
[tex]arccos(-1) = \theta[/tex]
[tex]180 = \theta[/tex]
[tex]180 = \pi[/tex] [tex]radians[/tex]
but it says [tex]\pi[/tex] isn't the right answer
But I don't think that sounds right, because [tex]\vec{A}[/tex] is at [tex]\arctan{\frac{1}{2}}[/tex] (26.7) degrees, and [tex]\vec{B}[/tex] runs along the negative X axis at 180 degrees, So that's a difference of 153.3 degrees. And if you convert that to radians, you get approximately [tex]\frac{17\pi}{20}[/tex] radians, which isn't right either.
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