Question

1) (25 pts) Using $\epsilon_{ijk}$ notation, evaluate $\nabla \cdot [($\vec{a} \times \vec{r}) \times \vec{a}]$ and $\nabla \times \vec{r}$ where $\vec{a}$ is an arbitrary constant vector and $\vec{r}$ is the position vector.

          1) (25 pts) Using $\epsilon_{ijk}$ notation, evaluate
$\nabla \cdot [($\vec{a} \times \vec{r}) \times \vec{a}]$ and $\nabla \times \vec{r}$
where $\vec{a}$ is an arbitrary constant vector and $\vec{r}$ is the position vector.

1) (25 pts) Using ϵijk notation, evaluate
∇· [(a⃗ ×r⃗) ×a⃗]and∇×r⃗wherea⃗is an arbitrary constant vector andr⃗is the position vector.

Added by Anthony M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ethan Deweese

Step 1

The dot product of a vector with itself is the square of the magnitude of the vector. So, a · a = |a|^2. Show more…

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Using notation, evaluate âˆš(a Â· a) and âˆš(F Â· F), where a is an arbitrary constant vector and F is the position vector.

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Question

1) (25 pts) Using $\epsilon_{ijk}$ notation, evaluate $\nabla \cdot [($\vec{a} \times \vec{r}) \times \vec{a}]$ and $\nabla \times \vec{r}$ where $\vec{a}$ is an arbitrary constant vector and $\vec{r}$ is the position vector.

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