Vector Fields:

Sketch the vector field \({\bf F} =x \, {\bf i} + y \, {\bf j}\)

Sketch the vector field \( \displaystyle{{\bf F} = \frac{y \, {\bf i} + x \, {\bf j}}{\sqrt{x^2+y^2}}}\)

Find the gradient vector field of (a) \(f(x,y)=x^2y^2-xy^3\)        (b)  \(f(x,y)=e^{x}\, \sin(3xy)\)

Find the gradient vector field of  \(f(x,y, z)= x^2 \ln(2y-5z)\)