s11wk01su - -6 x = x-3 2-9 Likewise 2 y 2 4 y = z 2-2 z = y...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 23, Summer I 2011 B. Dodson 1. Course Info 2. Week 1 Homework: 12.1: 3-Space, Distance 12.2 vectors: unit, standard unit, notations 12.3 dot product: orthogonal, proj, comp 12.4 cross product: formula, properties Problem 12.1.15: Show that the equation x 2 + y 2 + z 2 - 6 x + 4 y - 2 z = 11 represents a sphere, and Fnd its center and radius. Solution: ( x - a ) 2 = x 2 - 2 ax + a 2 , so the terms x 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: -6 x = ( x-3) 2-9 . Likewise, 2 y 2 + 4 y = . . . z 2-2 z = . . . y 2 + 4 y = ( y + 2) 2-4 z 2-2 z = ( z-1) 2-1, so x 2 + y 2 + z 2-6 x + 4 y-2 z = ( x-3) 2-9 + ( y + 2) 2-4 + ( z-1) 2-1 = 11 , or ( x-3) 2 + ( y + 2) 2 + ( z-1) 2 = 11 + 9 + 4 + 1 = 5 2 . conclusion: center = (3, -2, 1), radius = 5....
View Full Document

This note was uploaded on 11/24/2011 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

Page1 / 2

s11wk01su - -6 x = x-3 2-9 Likewise 2 y 2 4 y = z 2-2 z = y...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online