Curl of Product

[I'mLearning]

Do you know if [math]\mathbf{k}\cdot\nabla\times(\mathbf{a}\cdot\nabla\mathbf{a})[/math] can be rewritten?

If so, which rules are applied?

EDIT: The term seems to equal [math](\mathbf{a}\cdot\nabla\mathbf{k}\cdot\nabla\times\mathbf{a}) + (\mathbf{k}\cdot\nabla\times\mathbf{a}\nabla\cdot\mathbf{a})[/math] Can that be true?

 

[khansaheb]

Do you know if [math]\mathbf{k}\cdot\nabla\times(\mathbf{a}\cdot\nabla\mathbf{a})[/math] can be rewritten?

If so, which rules are applied?

EDIT: The term seems to equal [math](\mathbf{a}\cdot\nabla\mathbf{k}\cdot\nabla\times\mathbf{a}) + (\mathbf{k}\cdot\nabla\times\mathbf{a}\nabla\cdot\mathbf{a})[/math] Can that be true?

What is k and a? Are those related anyway?

 

[I'mLearning]

What is k and a? Are those related anyway?

hi khansaheb - k is the unit vector and a is any vector

 

[mario99]

Do you know if [math]\mathbf{k}\cdot\nabla\times(\mathbf{a}\cdot\nabla\mathbf{a})[/math] can be rewritten?

If so, which rules are applied?

EDIT: The term seems to equal [math](\mathbf{a}\cdot\nabla\mathbf{k}\cdot\nabla\times\mathbf{a}) + (\mathbf{k}\cdot\nabla\times\mathbf{a}\nabla\cdot\mathbf{a})[/math] Can that be true?

Hi I'mLearning,
not me I meant you!


Let [imath]\bold{k} = i + j + k[/imath] and let [imath]\bold{a} = 2i + 3j + 4k[/imath]

Solve the first form. Save your result for future comparison!

Solve the second form. Compare the two results. Are they equal?