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Chapter 14: Q. 3 (page 1095)

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

Short Answer

Expert verified

The inputs of a vector field in the Cartesian plane are points in the xy plane, where $$x,y\epsilon D$$.

Step by step solution

01

Step 1. Given Information

A vector field in the cartesian plane.

02

Step 2. Explanation

We know that the vector fields take the points on the cartesian plane as inputs.

So, the vector fields in the cartesian plane take points in the xy plane as their inputs.

Therefore, for a function $$f(x,y)$$ having the domain $$D$$ have their inputs equal to $$x,y\epsilon D$$.

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Most popular questions from this chapter

ComputethedivergenceofthevectorfieldsinExercises17–22.F(x,y,z)=xeyzi+yexzj+zexyk

Compute a general formula for dS for any planeax+by+cz=kifc≠0.

F(x,y,z)=−xzi−yzj+z2k, where S is the cone with equation z=x2+y2between z=2,4, with n pointing outwards.

Give a formula for a normal vector to the surface S determined by x = f(y, z), where f(y, z) is a function with continuous partial derivatives.

Find

∫S F(x,y,z)⋅ndSifF(x,y,z)=ln⁡x2+y2+1z+3i+yy+1j+ez2k

Where S is the portion of the sphere with radius 2, centered at the origin, and that lies below the plane with equation z=-2, with n pointing outwards.

See all solutions

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