Curly

Calculus Level 3

Consider the vector field

F(x,y,z)=xsinzi+ycosxj+ztanyk \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 (7π6,π6,2π3) ( \frac{7\pi}{6}, \frac{\pi}{6}, \frac{2\pi}{3}) can be expressed in the form ai+bj+ck a \, \mathbf{i} + b \, \mathbf{j} + c \, \mathbf{k} where a a , b b and c c are real numbers. a+b+c a + b + c can be expressed in the form deπ \frac{d}{e} \pi where d d and e e are coprime positive integers. What is d+e 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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