Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find the point on the sphere x² + y² + z² = 16 farthest from the point (-1,-1,1). The point is .. (Type an ordered triple.)

Find the point on the sphere x² + y² + z² = 16 farthest from the point (-1,-1,1). The point is .. (Type an ordered triple.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
See similar textbooks
icon
Related questions
Question
100%
### Problem Statement Find the point on the sphere \( x^2 + y^2 + z^2 = 16 \) farthest from the point \((-1, -1, 1)\). ### Solution The point is \(\left( \_\_, \_\_, \_\_ \right)\). (Type an ordered triple.) --- This problem is centered on identifying the point on a given sphere that is the greatest distance away from a specified point in three-dimensional space. The equation of the sphere \( x^2 + y^2 + z^2 = 16 \) represents a sphere centered at the origin \((0,0,0)\) with a radius of 4 units. The specific point from which the distance is to be maximized is \((-1, -1, 1)\). To find the farthest point, one typically needs to apply concepts from calculus or geometry, such as the dot product in vector mathematics or the use of Lagrange multipliers.
Transcribed Image Text:### Problem Statement Find the point on the sphere \( x^2 + y^2 + z^2 = 16 \) farthest from the point \((-1, -1, 1)\). ### Solution The point is \(\left( \_\_, \_\_, \_\_ \right)\). (Type an ordered triple.) --- This problem is centered on identifying the point on a given sphere that is the greatest distance away from a specified point in three-dimensional space. The equation of the sphere \( x^2 + y^2 + z^2 = 16 \) represents a sphere centered at the origin \((0,0,0)\) with a radius of 4 units. The specific point from which the distance is to be maximized is \((-1, -1, 1)\). To find the farthest point, one typically needs to apply concepts from calculus or geometry, such as the dot product in vector mathematics or the use of Lagrange multipliers.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS