The calculated vectors are:
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4)
[tex]\vec{B}-\vec{C}[/tex]=(-5,4,0)
[tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3)
[tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)
Generally, the equation for is mathematically given a
[tex]\vec{V}+\vec{W}=\left(V_1, V_2, V_3\right)+\left(W_1, W_2, W_3\right)\\\\\vec{V}+\vec{W}=\left(V_1+W_1, V_2+W_2, V_3+W_3\right) \text { }[/tex]
[tex]\vec{V}-\vec{W}=\left(V_1, V_2, V_3\right)-\left(W_1, W_2, W_3\right)\\\\\vec{V}-\vec{W}=\left(V_1-W_1, V_2-W_2, V_3-W_3\right)[/tex]
[tex]\alpha \cdot \vec{V}=\alpha \cdot\left(V_1, V_2, V_3\right)\\\\\alpha \cdot \vec{V}=\left(\alpha \cdot V_1, \alpha \cdot V_2, \alpha \cdot V_3\right)[/tex]
[tex]\vec{A}-\vec{B}=(1,0,-3)-(-2,5,1)\\\vec{A}-\vec{B}=(3,-5,-4) \\\\&\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)\\&\vec{B}-\vec{C}=(-5,4,0) \\\\&-\vec{A}+\vec{B}-\vec{C}=-(1,0,-3)+(-2,5,1)-(3,1,1)\\-\vec{A}+\vec{B}-\vec{C}=(-6,4,3) \\\\&3 \vec{A}-2 \vec{C}=3(1,0,-3)-2(3,1,1)\\3 \vec{A}-2 \vec{C}=(3,0,-9)-(6,2,2)\\3 \vec{A}-2 \vec{C}=(-3,-2,-11)[/tex]
In conclusion,
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CQ
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.
