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Chapter 1: Q15P (page 18)
Calculate the divergence of the following vector functions:
(a) The divergence is 0.
(b) The divergence is .
(c) The divergence is.
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(a) Check product rule (iv) (by calculating each term separately) for the functions
(b) Do the same for product rule (ii).
(c) Do the same for rule (vi).
Compute the line integral of
along the triangular path shown in Fig. 1.49. Check your answer using Stokes' theorem. [Answer:8/3]
Compute the divergence of the function
Check the divergence theorem for this function, using as your volume the inverted hemispherical bowl of radius R,resting on the xyplane and centered at the origin (Fig. 1.40).
(a) If A and B are two vector functions, what does the expression mean?(That is, what are its x, y, and z components, in terms of the Cartesian componentsof A, B, and V?)
(b) Compute , where is the unit vector defined in Eq. 1.21.
(c) For the functions in Prob. 1.15, evaluate .
Use the cross product to find the components of the unit vector perpendicular to the shaded plane in Fig. 1.11.
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