Question

Problem 5 Orient the curve $C \subset \mathbb{R}^3$ at the intersection of the cone $z^2 = x^2 + y^2$ and the plane $2z = y + 4$, counter-clockwise (when viewed from above). Calculate the circulation $W_C = \oint_C \mathbf{F} \cdot d\mathbf{r}$ over $C$ in this orientation, for the vector field $\mathbf{F}(x, y, z) = (4z - 4y, e^{z^4} - 2x, \sin(y^3) + 3z)$.

          Problem 5
Orient the curve $C \subset \mathbb{R}^3$ at the intersection of the cone $z^2 = x^2 + y^2$ and the plane $2z = y + 4$, counter-clockwise
(when viewed from above). Calculate the circulation $W_C = \oint_C \mathbf{F} \cdot d\mathbf{r}$ over $C$ in this orientation, for the vector field
$\mathbf{F}(x, y, z) = (4z - 4y, e^{z^4} - 2x, \sin(y^3) + 3z)$.

Problem 5
Orient the curve C ⊂ℝ^3 at the intersection of the cone z^2 = x^2 + y^2 and the plane 2z = y + 4, counter-clockwise
(when viewed from above). Calculate the circulation WC = 𝐅· d𝐫 over C in this orientation, for the vector field
𝐅(x, y, z) = (4z - 4y, e^z^4 - 2x, sin(y^3) + 3z).

Added by Sheila D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/21/2023

Step 1

This gives us: $$(y+4)^2/4 = x^2 + y^2$$ Show more…

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Problem 5 Orient the curve $C \subset \mathbb{R}^3$ at the intersection of the cone $z^2 = x^2 + y^2$ and the plane $2z = y + 4$, counter-clockwise (when viewed from above). Calculate the circulation $W_C = \oint_C \mathbf{F} \cdot d\mathbf{r}$ over $C$ in this orientation, for the vector field $\mathbf{F}(x, y, z) = (4z - 4y, e^{z^4} - 2x, sin(y^3) + 3z)$.