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### Section 5-1 : Vector Fields

1. Sketch the vector field for $$\vec F\left( {x,y} \right) = 2x\,\vec i - 2\vec j$$. Solution
2. Sketch the vector field for $$\vec F\left( {x,y} \right) = \left( {y - 1} \right)\,\vec i + \left( {x + y} \right)\vec j$$. Solution
3. Compute the gradient vector field for $$f\left( {x,y} \right) = {y^2}\cos \left( {2x - y} \right)$$. Solution
4. Compute the gradient vector field for $$\displaystyle f\left( {x,y,z} \right) = {z^2}{{\bf{e}}^{{x^{\,2}} + 4y}} + \ln \left( {\frac{{xy}}{z}} \right)$$. Solution