Chapter 13: Q6TF (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.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
\(\int\limits_{\rm{C}} {} {\rm{(y + z)dx + (x + z)dy + (x + y)dz}}\)
\({\rm{C}}\) consists of line segments from \({\rm{(0,0,0)}}\) to \({\rm{(1,0,1)}}\) and from \({\rm{(1,0,1)}}\) to \({\rm{(0,1,2)}}\).
Find the area of the surface.
The part of the plane \(x + 2y + 3z = 1\) that lies inside the cylinder \({x^2} + {y^2} = 3\) .
Evaluate the line integral\(\int_{\rm{C}} {\rm{F}} {\rm{ \times dr}}\)where\({\rm{C}}\)is given by the vector function\({\rm{r(t)}}\).
\(\begin{array}{c}{\rm{F(x,y,z) = sinxi + cosyj + xzk,}}\\{\rm{r(t) = }}{{\rm{t}}^{\rm{3}}}{\rm{i - }}{{\rm{t}}^{\rm{2}}}{\rm{j + tk,}}\;\;\;{\rm{0}} \le {\rm{t}} \le {\rm{1}}\end{array}\)
Evaluate the line integral\(\int_{\rm{C}} {\rm{F}} {\rm{ \times dr}}\) where \({\rm{C}}\)is given by the vector function\({\rm{r(t)}}\).
\(\begin{array}{c}{\rm{F(x,y,z) = xi + yj + xyk,}}\\{\rm{r(t) = costi + sintj + tk,}}\;\;\;{\rm{0}} \le {\rm{t}} \le {\rm{\pi }}\end{array}\)
To determine: The area of the surface \(y = {x^3},0 \le x \le 2\) rotating about \(x\)-axis.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
