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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

If r = ⟨x, y, z⟩ and r0 = ⟨x0, y0, z0⟩, describe the set of all points (x, y, z) such that | rr0 | = 1.

To determine

To describe: All set of points for condition |rr0|=1.

Explanation

Given:

Two three-dimensional vectors r=x,y,z and r0=x0,y0,z0.

Definitions:

Subtraction of vectors:

Consider the two three-dimensional vectors such as a=a1,a2,a3 and b=b1,b2,b3.

The vector subtraction of two vectors (ab) is,

(ab)=a1,a2,a3b1,b2,b3=a1b1,a2b2,a3b3

Formula used:

Consider the expression for magnitude of vector a=a1,a2,a3(|a|).

|a|=a12+a22+a32 (1)

Write the expression for sphere with center C(h,k,l) and radius r.

(xh)2+(yk)2+(zl)2=r2 (2)

Write the expression for relation between vectors r and r0.

|rr0|=1

From definition, substitute x,y,z for r and x0,y0,z0 for r0,

|x,y,zx0,y0,z0|=1

|xx0,yy0,zz0|=1 (3)

Find the value of |xx0,yy0,zz0| by using equation (1)

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Chapter 12 Solutions

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P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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