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Chapter 10: Q 34 (page 789)

Find the equation of a sphere containing the point (1, 4, 7) and whose center is (-2, 3, 5).

Short Answer

Expert verified

The required equation is:(x+2)2+(y-3)2+(z-5)2=14

Step by step solution

01

Given information

A sphere containing the point (1, 4, 7) and whose center is (-2, 3, 5).

02

Finding the radius

The radius will be the distance between the center and the point given.

Radius is:

(1+2)2+(4-3)2+(7-5)2

Simplify:

14

03

Finding the equation

The equation of the sphere may be written as:

(x+2)2+(y-3)2+(z-5)2=(14)2

Simplify:

(x+2)2+(y-3)2+(z-5)2=14

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Most popular questions from this chapter

In Exercises 24-27, find compuv,projuv and the component of v orthogonal tou.

role="math" localid="1649693816584" u=3,1,-2,v=-6,-2,4

What is a parallelepiped? What is meant by the parallelepiped determined by the vectors u, v and w? How do you find the volume of the parallelepiped determined by u, v and w?

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,−2),Q(−2,0),R(1,−5)

(Hint: Think of the xy-plane as part of ℝ3.)

Find u+vandu-valso sketch u,v,u+v,u-v

u=4,0andv=0,3

If u and v are vectors in ℝ3 such that u×v=v×u, what can we conclude about u and v?
See all solutions

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