Given = (x, y, z) and F = F(x, y, z), put H = times and h = .( times F). Then Bo

Question

Given = (x, y, z) and F = F(x, y, z), put H = times and h = .( times F). Then Both H = 0 and h = 0, since the expressions curl (grad ) and div(curl F) always vanish. H = 0. but h may be non-zero. H may be non-zero, but h = 0. Both of H and h may be non-zero. Let F(x, y) = 2yi + 2xj = (2y, 2x) and G(x, y) = 2i + 3j = (2, 3) be vector fields defined over the entire plane. Then: F is conservative with potential function x2 + y2 but G is not conservative F is conservative with potential function 2xy but G is not conservative F is conservative with potential 2xy and G is conservative with potential 2x + 3y F is not conservative but G is conservative with potential 2x + 3y

Explanation / Answer

the correct answer is a & c

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