Problem 5. Gradient. Calculate the gradient of the following scalar fields: (a) U = xy +...

 

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Problem 5. Gradient. Calculate the gradient of the following scalar fields: (a) U = x²y + xyz (b) V = pz sin o + z² cos? o + p? (c) f = cos 0 sin o Inr +r2o Problem 6. Gradient. If ř = xũ, + yü, + zü, is the position vector of point (x,y,z), r = |F), and n is an integer, show that Vr" = nr"-2F. %3! Problem 5. Gradient. Calculate the gradient of the following scalar fields: (a) U = x²y + xyz (b) V = pz sin o + z² cos? o + p? (c) f = cos 0 sin o Inr +r2o Problem 6. Gradient. If ř = xũ, + yü, + zü, is the position vector of point (x,y,z), r = |F), and n is an integer, show that Vr" = nr"-2F. %3!