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Chapter 14: Q. 5 (page 1095)

What are the outputs of a vector field in the Cartesian plane?

Short Answer

Expert verified

The outputs of a vector field in the Cartesian plane is vectors.

Step by step solution

01

Step 1.Given Information

What are the outputs of a vector field in the Cartesian plane?

02

Step 2. The outputs of a vector field in the Cartesian plane 

We've looked at two- and three-variable functions with a numerical output. We could also write functions with a vector output.

A vector field is a function that assigns a vector to each point in its domain. Thus, a vector field in the plane has outputs that are vectors in the xy-plane

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Most popular questions from this chapter

How would you show that a given vector field in ℝ2 is not conservative?

Find∫S 1dS, where S is the portion of the surface determined byz=x2−3ythat lies above the region in the xy-plane bounded by the x-axis and the lines with equationsy=2x,x=3.

What are the outputs of a vector field in ℝ3?

Find the masses of the lamina:

The lamina occupies the region of the hyperboloid with equation z2+4=x2+y2 that lies above and/or below the disk of radius 5 about the origin in the XY-plane, and the density function, ρ(x, y,z), is proportional to the distance from the origin.

What is the difference between the graphs of

G(x,y)=xi+yjandF(x,y)=−xi+(-y)j
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