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- F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?Sketch the vector field. F(2, y) = (-2 2. * y 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -3- -4+ Clear All Draw: 2.Fill in the table and then sketch the vector field. y F(x, y) = -2 -2 -2 2 -2 -2 -2 3- -2- 2. /- 2.
- Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point in a 3D space.Sketch the vector field. A x 2 0 0 2 -2 0 -2 y 0 2 ♡ -2 2 -2 -2 2 -2 q F(x, y) = (22) Clear All Draw: 3 2 1 -1 -2 -3 -4 NFind the curl of the vector field F. F= (x-y+z)i+ (6x-y+7z)j+ (9x+ 6y + z)k curl F = i+
- Sketch the vector field. x|y|F(x, y) = = 0 -4 2 02 -2 0 -2 2 2 -2 0 -3 -2 2 -2 -2 № → 3 2 1 -2 ین Y " X 2 1 2 3 +y² i+ 4z4 7x+y (2,-4, -1)? Enter an exact answer. Let F(x, y, z) = = -6x - 8y Provide your answer below: k x5 -k be a vector field in R³. What vector is associated with the point y³ -j+Sketch the vector field. F(7, v) = ( -5 - | 2 -2 -2 2 2 -2 2 -2 -2 -2 4+ -4 -3 -2 -1 3 -2- -3 -4 Clear All Draw: 2. 2. 2. 2.
- Let F = sin (2x + 4z)i – 8ye* k. Calculate div(F) and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.) div(F) = (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) curl(F) =Sketch the vector field in the xy-plane. F = -713 у y X X у у X х XLet (z, y, z)= + z ln (y + 2) be a scalar field. Find the directional derivative of at P(2,2,-1) in the direction of the vector 12 4 Enter the exact value of your answer in the boxes below using Maple syntax. Number