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(a) Compute the curl of the vector field vector F = < x y + z^2, x^2, x z - 2 >. (b) What is the...

Question:

(a) Compute the curl of the vector field {eq}\displaystyle \vec F = \langle x y + z^2,\ x^2,\ x z - 2 \rangle {/eq}.

(b) What is the curt at the point {eq}(0,\ -1,\ 0) {/eq}.

(c) Is this vector field irrational or not?

Curl of a Vector Field

Curl of a vector field is given by evaluating the cross product.

{eq}CurlF= \bigtriangledown\times F= (\dfrac{\partial }{\partial x}+\dfrac{\partial }{\partial y}+\dfrac{\partial }{\partial z})\times F\\ {/eq}

For a vector field to be irrotational, the curl of the vector should be zero at all points.

Answer and Explanation:

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Finding The Cross Product of Two Vectors

from Physics: High School

Chapter 2 / Lesson 12
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