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Chapter 13: Q17E (page 760)

Match the vector field F on \({{\rm{R}}^{\rm{3}}}\)with the plots labelled I–IV. Give reasons for your choices.

\(F(x,y,z) = xi + yj + 3k\)

Short Answer

Expert verified

The vector field \(F\) matches with the plot III.

Step by step solution

01

Given Information.

The given vector field is \(F(x,y,z){\rm{ }} = {\rm{ }}xi + yj + 3k\).

02

Select the matching plot and give reason.

It has a constant z component and x and y are variable.

The lines in the given vector field do not change with z, but depend linearly on x and y for the lines' x and y components.

The z component is \(3\) for all (x,y,z) then the vector should point towards positive z-direction and x and y varies. The vectors are not parallel.

Therefore, the vector field \(F\) matches with the plot III.

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Most popular questions from this chapter

Show that the line integral is independent of path and evaluate the integral.

\(\int_C 2 x{e^{ - y}}dx + \left( {2y - {x^2}{e^{ - y}}} \right)dy\), \(C\) is any path from \((1,0)\) to \((2,1)\)

To determine: The area of the surface \(y = {x^3},0 \le x \le 2\) rotating about \(x\)-axis.

Find the value of\(\iint_{H}{f}(x,y,z)dS \)..

Find the value of \(\iint_{S}{f}(x,y,z)dS \).

Match the vector field F with the plots labelled I–IV. Give reasons for your choices.

\(F(x,y) = \left\langle {y,x - y} \right\rangle \)
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