Mcfarlane Sherman
10/19/2023 · Senior High School
Let \( F=(y \cos 2 x) i+\left(y^{2} \sin 2 x\right) j+\left(x^{2} y+z\right) \mathbf{k} \). Is there a vector field \( \mathbf{A} \) such that \( F=\nabla \times \mathbf{A} \) ? Select the correct choice below and fill in the answer boxes within your choice. A. No, because the divergence of \( F \) is \( \square \), but the divergence of the curl of any vector field is always \( \square \). B. Yes, because the divergence of \( F \) is \( \square \) which is also the divergence of the curl of any vector field.
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A. No, because the divergence of \( F \) is 1, but the divergence of the curl of any vector field is always 0.
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