Let F = yi + xj + x³y³ z³k, C the curve x2 + y² + 6x – 2y + 9 = 0, z = 2 (with counterclockwise orientation looking from the direction of the positive z-axis). Calculate the line integral - F· dR. C

Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

Q: Determine whether the line integral of each vector field (in blue) along the oriented path (in red)…

A: To find- Determine whether the line integral of the vector field, along the oriented path is…

Q: hank you

A: Given,      θ˙=sin2θ

Q: function r(t). The temperature at the point (x, y) is given by f(x, y) = 3x + 4y + 20. The velocity…

A: Introduction: In mathematics, a derivative is the rate at which a function changes in relation to a…

Q: Determine whether the line integrals of the vector fields along the oriented curves are positive or…

A: Since the line integral is a dot product.When the angle between the direction field of flow and…

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Find the divergence of the vector field F = div F =

A:

Q: Show that the gradient vector is perpendicular to the tangent at a point of an isovalue curve

A: According to question                                     Let,  w=f(x, y, z)  be a function in…

Q: Find the parametrization of two different curves from the point (2,4) to (3,9). Compute the work…

A: Given point (2,4)  and (3,9)now equationof line passing through two point is given by…

Q: What is the geometrical meaning of an integral of a vector function?

A: We can realize geometric meaning of integration such as

Q: 1. Let F =i+y^2j +z^4k. Find the general flow lines for this vector field. Present the flow line…

A: Consider the provided question,

Q: Find the divergence of the vector field F - div F = =

A:

Q: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

A:

Q: Find the curl of the vector field F = curl F - i.

A:

Q: Find the divergence of the vector field F =< yx³, xzª, zy² div F = V

A: Given : F→=&lt;yx3,xz4,zy2&gt;   To Find : Divergence of given vector field