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Chapter 12: Q. 72 (page 918)

Let w=f(x,y,z)be a function of three variables. Prove that when c1鈮�c2, the level surfaces defined by the equations f(x,y,z)=c1 andf(x,y,z)=c2 do not intersect

Short Answer

Expert verified

We proved by contradictions that the equations do not intersect

Step by step solution

01

Given information

We are given a function of three variablesw=f(x,y,z)

02

Explanation

Let the function can be given as

ax+by+dz=c1andax+by+dz=c2

Let these two function be intersecting and point of intersection is (x0,y0,z0)

Substituting the equations becomes

ax0+by0+dz0=c1andax0+by0+dz0=c2

As the left hand side is equal then the right hand side should also be equal and we get,

c1=c2

But we are given c1鈮�c2

hence our assumption is wrong

The equations do not intersect

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