Question

find $\int_{C} \vec{F} \cdot d \vec{r}$ where $C$ is a circle of radius 2 in the plane $x+y+z=3,$ centered at (1,1,1) and oriented clockwise when viewed from the origin. $$\overrightarrow{\boldsymbol{F}}=\overrightarrow{y \vec{i}}-x \vec{j}+(y-x) \vec{k}$$

          find $\int_{C} \vec{F} \cdot d \vec{r}$ where $C$ is a circle of radius 2 in the plane $x+y+z=3,$ centered at (1,1,1) and oriented clockwise when viewed from the origin.
$$\overrightarrow{\boldsymbol{F}}=\overrightarrow{y \vec{i}}-x \vec{j}+(y-x) \vec{k}$$

Added by Jose W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/12/2022

Step 1

We can parameterize this circle as follows: $\vec{r}(t) = (1+2\cos(t))\vec{i} + (1+2\sin(t))\vec{j} + (1-2\cos(t)-2\sin(t))\vec{k}$ for $0 \leq t \leq 2\pi$. Show more…

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find $\int_{C} \vec{F} \cdot d \vec{r}$ where $C$ is a circle of radius 2 in the plane $x+y+z=3,$ centered at (1,1,1) and oriented clockwise when viewed from the origin. $$\overrightarrow{\boldsymbol{F}}=\overrightarrow{y \vec{i}}-x \vec{j}+(y-x) \vec{k}$$