Ramos Evans
07/07/2023 · High School
Question 3 finding a potential for it. (a) Find the volume of the parallelopiped whose coterminus edges are given by the vectors \( \left.\vec{A}=2 \vec{i}-e^{x} \cos y+y z\right) \vec{i}+\left(x z-e^{x} \sin y\right) \vec{j}+(x y+z) \vec{k} \) is conservative by \( 3 \vec{j}+4 \vec{k}, \vec{B}=\vec{i}+2 \vec{j}-\vec{k} \) and \( \vec{C}=3 \vec{i}-\vec{j}+2 \vec{k} \).
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The volume of the parallelepiped defined by the vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) is given by the absolute value of the expression \(6 - 3e^x \cos y + 3yz - 5xz + 5e^x \sin y - 7xy - 7z\).
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