Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi – y²zj + 2xz²k and V = xi – 2zk. Then verify the following relations 1. div(fU) = fdiv(U) + U · Vf 2....

Q: Solve on white page clean and stepwise:<br>Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi – y²zj + 2xz²k and V = xi – 2zk. Then<br>verify the following relations<br>1. div(fU) = fdiv(U) + U · Vf<br>2. div(gradf) = 7?f<br>3. div(fVg) = fV²g+Vf•Vg<br>4. div(U × V) = V· curlU – U · curlV<br>5. curl(curlU) = grad(divU) – V²U<br>

Extracted text: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi – y²zj + 2xz²k and V = xi – 2zk. Then verify the following relations 1. div(fU) = fdiv(U) + U · Vf 2. div(gradf) = 7?f 3. div(fVg) = fV²g+Vf•Vg 4. div(U × V) = V· curlU – U · curlV 5. curl(curlU) = grad(divU) – V²U

Jun 03, 2022

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Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi – y²zj + 2xz²k and V = xi – 2zk. Then verify the following relations 1. div(fU) = fdiv(U) + U · Vf 2....

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