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Vectors $\vec{A}, \vec{B}$, and $\vec{C}$ are such $\vec{A} \cdot \vec{B}=0$ $\vec{A} \cdot \vec{C}=0$. Then the vector parallel is $\vec{A}$ is:
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Verified Answer
The correct answer is:
$\vec{B} \times \vec{C}$
From vector produce
$$
\vec{A} \times(\vec{B} \times \vec{C})=(\vec{B} \cdot \vec{C}) \vec{B}-(\vec{A} \cdot \vec{B}) \vec{C}
$$
Given that $\vec{A} \cdot \vec{B}=0, \vec{A} \cdot \vec{C}=\mathrm{C}$ then $\vec{A} \times(\vec{B} \times \vec{C})=0$ thus vector $A$ is paralles to $\vec{B} \times \vec{C}$
$$
\vec{A} \times(\vec{B} \times \vec{C})=(\vec{B} \cdot \vec{C}) \vec{B}-(\vec{A} \cdot \vec{B}) \vec{C}
$$
Given that $\vec{A} \cdot \vec{B}=0, \vec{A} \cdot \vec{C}=\mathrm{C}$ then $\vec{A} \times(\vec{B} \times \vec{C})=0$ thus vector $A$ is paralles to $\vec{B} \times \vec{C}$
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