Chapter 13: Q7TF (page 830)
If \({\rm{F}}\)and\({\rm{G}}\)are vector fields and\({\rm{div F = div G}}\), then\({\rm{F = G}}\).
The given statement is false.
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Find the value of\(\iint_S ydS\)
Evaluate the line integral, where \({\rm{C}}\)is the given curve.
\(\int_{\rm{C}} {{{\rm{z}}^{\rm{2}}}} {\rm{dx + }}{{\rm{x}}^{\rm{2}}}{\rm{dy + }}{{\rm{y}}^{\rm{2}}}{\rm{dz}}\)\(C\) Is the line segment from?
\({\bf{F}} = |{\bf{r}}{|^2}{\bf{r}}\), where \({\bf{r}} = x{\bf{i}} + y{\bf{j}} + z{\bf{k}}\), \(S\) is the sphere with radius \(R\) and centre the origin
Find the area of the surface with the vector equation
\({\rm{r}}(u,v) = \left\langle {{{\cos }^3}u{{\cos }^3}v,{{\sin }^3}u{{\cos }^3}v,{{\sin }^3}v} \right\rangle ,0 \le u \le \pi ,0 \le v \le 2\pi \). State your answer correct to four decimal places.
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