Find such that
⃗ = (3 − 2 + )⃗ + (4 + − )⃗ + ( − + 2)
⃗⃗ is solenoidal
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where a and b are constants. Find a and b such that v is both solenoidal and irrotational.
For this problem I've taken the divergence and the curl of this vector field, and found six distinct equations in a and b. I've discarded x,y,z and I currently have lots of eqns for only 2 unknowns. I'm finding it really hard to find a solution to all the eqns simultaneously, partly because there's so many abut also because the eqns are a bit complex, involving quadratic terms (so hence a lot of poss. unknowns).
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