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3. Consider a vector field, \( \vec{F}(\vec{r})=\hat{k} \times \vec{r} \). a. Cridite: directly the line integral of the given vector field around a circle in the \( x-y \) plane, centered at the origin with radius \( r \). [7 marks] b. Calculate the line integral by using the Stoke's theorem. [4 marks] 1

          3. Consider a vector field, \( \vec{F}(\vec{r})=\hat{k} \times \vec{r} \).
a. Cridite: directly the line integral of the given vector field around a circle in the \( x-y \) plane, centered at the origin with radius \( r \).
[7 marks]
b. Calculate the line integral by using the Stoke's theorem.
[4 marks]
1

3. Consider a vector field, F⃗(r⃗)=k̂×r⃗.
a. Cridite: directly the line integral of the given vector field around a circle in the x-y plane, centered at the origin with radius r.
[7 marks]
b. Calculate the line integral by using the Stoke's theorem.
[4 marks]
1

Added by Crystal G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Heba Qureshi

Step 1

Step 1: **Understand the Vector Field** The vector field is given by \( \vec{F}(\vec{r}) = \hat{k} \times \vec{r} \), where \( \vec{r} = x\hat{i} + y\hat{j} + z\hat{k} \). Show more…

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3. Consider a vector field, \( \vec{F}(\vec{r})=\hat{k} \times \vec{r} \). a. Cridite: directly the line integral of the given vector field around a circle in the \( x-y \) plane, centered at the origin with radius \( r \). [7 marks] b. Calculate the line integral by using the Stoke's theorem. [4 marks] 1