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Find curl F for the vector field F = z\sin x i -2x\cos y j +y\tan z k at the point ...

Question:

Find {eq}curl \mathbf F {/eq} for the vector field {eq}\mathbf F = z\sin x \mathbf i -2x\cos y \mathbf j +y\tan z \mathbf k {/eq} at the point {eq}(\pi, 0, \pi/4) {/eq}

The Curl and the Divergence:

In this problem, we need to find out the curl and the divergence of the given vector field. Now the curl and the divergence of the vector field {eq}F=<P,Q,R> {/eq} is:

{eq}Curl \vec{F} =\begin{vmatrix} i & j & k \\ \dfrac{\partial}{ \partial x} & \dfrac{\partial}{ \partial y} & \dfrac{\partial}{ \partial z} \\ P & Q & R \end{vmatrix} {/eq}

Next, plug in the given point to get the desired solution.

Answer and Explanation:

We are given:

{eq}\mathbf F = z\sin x \mathbf i -2x\cos y \mathbf j +y\tan z \mathbf k {/eq}

{eq}Curl \vec{F} =\begin{vmatrix} i & j & k...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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