Question
Use a parallelepiped to show that $\vec{a} \cdot(\vec{b} \times \vec{c})=(\vec{a} \times \vec{b}) \cdot \vec{c}$ for any vectors $\vec{a}, \vec{b},$ and $\vec{c}$
Step 1
The cross product $\vec{b} \times \vec{c}$ gives us a vector that is perpendicular to both $\vec{b}$ and $\vec{c}$, and its magnitude is equal to the area of the parallelogram formed by $\vec{b}$ and $\vec{c}$. Show more…
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Key Concepts
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