[amp_mcq option1=”-14zi – 2x2k” option2=”6zi + 4x2j – 2x2k” option3=”-14zi + 6yj + 2x2k” option4=”6zi – 8xyj + 2x2yk” correct=”option1″]<\/p>\n
The curl of a vector field is a vector field that describes the circulation of a fluid around a point. It is calculated using the following formula:<\/p>\n
$$\\text{curl}(F) = \\det \\begin{pmatrix} \\hat{\\imath} & \\hat{\\jmath} & \\hat{k} \\\\ \\dfrac{\\partial}{\\partial x} & \\dfrac{\\partial}{\\partial y} & \\dfrac{\\partial}{\\partial z} \\\\ F_x & F_y & F_z \\end{pmatrix}$$<\/p>\n
In this case, the vector field is $F(x, y, z) = 2x^2y + 5z^2j – 4uyzk$. Substituting this into the formula for the curl, we get:<\/p>\n
$$\\text{curl}(F) = \\det \\begin{pmatrix} \\hat{\\imath} & \\hat{\\jmath} & \\hat{k} \\\\ \\dfrac{\\partial}{\\partial x} & \\dfrac{\\partial}{\\partial y} & \\dfrac{\\partial}{\\partial z} \\\\ 2x^2 & 5z^2 & -4uy \\end{pmatrix} = -14zi – 2x^2k$$<\/p>\n
Therefore, the curl of the vector field is $-14zi – 2x^2k$.<\/p>\n
Here is a brief explanation of each option:<\/p>\n
[amp_mcq option1=”-14zi – 2x2k” option2=”6zi + 4x2j – 2x2k” option3=”-14zi + 6yj + 2x2k” option4=”6zi – 8xyj + 2x2yk” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20217","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n