# Curly

Calculus Level 3

Consider the vector field

$\mathbf{F}(x, y, z) = x\sin{z} \, \, \mathbf{i} + y\cos{x} \, \, \mathbf{j} + z\tan{y} \, \, \mathbf{k}$.

The curl of this vector field at the point $( \frac{7\pi}{6}, \frac{\pi}{6}, \frac{2\pi}{3})$ can be expressed in the form $a \, \mathbf{i} + b \, \mathbf{j} + c \, \mathbf{k}$ where $a$, $b$ and $c$ are real numbers. $a + b + c$ can be expressed in the form $\frac{d}{e} \pi$ where $d$ and $e$ are coprime positive integers. What is $d + e$?

If you are unfamiliar with the concept of curl you may wish to read the following webpage.

Curl Explanation

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