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latentcorpse
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hi. the is it true that if \vec{m} is a constant vector, then
\nabla \cdot \vec{m}=0?
\nabla \cdot \vec{m}=0?
Gradient Ques: Is Constant Vector Dot Product 0?
- Thread starter latentcorpse
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If \(\vec{m}\) is a constant vector, then the divergence of \(\vec{m}\) is indeed zero, meaning \(\nabla \cdot \vec{m} = 0\). This is because the gradient of a constant vector field does not change, resulting in no variation across the field. Therefore, the dot product of a constant vector with itself remains constant and does not yield any directional change. The discussion confirms that the mathematical properties of constant vectors lead to a divergence of zero. Understanding this principle is essential in vector calculus and related fields.
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