Express the vector field W=(x^2-y^2)i +xzk in cylindrical coordinates at P(6,60degrees,-4).
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Express the vector field W=(x^2-y^2)i +xzk in cylindrical coordinates at P(6,60degrees,-4).
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- solve only ( 4 ,5 ,6 )For vector field v(x, y) = (-xy, y), find all points P such that the amount of fluid flowing in to Pequals the amount of fluid flowing out of P. Select the correct answer below: O At all points P O At all points P, where y s0 O At all points P, where y = 1 O At all points P, where y = xCalculate the flux of vector field F = (xy°, x²y) across the circle of radius 1 centered at coordinates (0, –1).
- Calculate the flux of the given vector field by evaluating the line integral directly alongthe given curve for the below parts:(a) The vector field is ⃗ F = (x − y)⃗i + x⃗j. The curve is the circle x^2 + y^2 = 1in the xy-plane. Use the parameterization x = cos t and y = sin t.(b) The vector field is ⃗ F = (x − 1)⃗i + y⃗j. The curve is a circle of radius 3centered at (1, 1). The parametric form of this circle is⃗r = (1 + 3 cos t)⃗i + (1 + 3 sin t)⃗j, 0 ≤ t ≤ 2π(c) The vector field is ⃗F = x⃗i + y⃗j. The curve is the line segment from thepoint (0, 1) to the point (1, 3).Find the flux of F = xi - 2yj + zk across the portion of cylinder x² + z² = 9 in the first and forth octants. (3,-3,0) n X (0,0,3) (3,0,0) (0,3,0) yFind a polar equation for the conic Parabola with its focus at the pole and the given vertex (3, π).
- Compute the flux of the vector field F = 2zk through S, the upper hemisphere of radius 5 centered at the origin, oriented outward. flux =Calculate the flux of the vector field F(x, y, z) = 5i + 5j + zk through the closed circular cylinder of radius 4 centered about the z-axis for -6 ≤ z < 6, oriented away from the z-axis. Note: a closed cylinder has a top and a bottom. Flux = SS F.dĀ=Evaluate the surface integral F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = −xi - yj + z³k, S is the part of the cone z = √x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √√x² + y² xx 0 z=4