{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAC2313 T1Solutions

# MAC2313 T1Solutions - MAS 2313-03 Test 1 Fall 2007 Name...

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

MAS 2313-03 Test 1 Fall 2007 Name: Show all work (No credit given if work is not shown). 7 points each unless indicated otherwise. 1. Write an equation of the sphere that passes through the point (1 , 1 , 2) and whose center is (2 , 3 , 4). The radius is the distance between (1 , 1 , 2) and (2 , 3 , 4), i.e. r = 1 + 4 + 4 = 3 Hence an equation for the sphere is ( x 2) 2 + ( y 3) 2 + ( z 4) 2 = 9. 2. Describe the set of all points ( x, y, z ) that satisfy x 2 + y 2 + z 2 6 x + 2 y 4 z = 0. Completing the square we get ( x 3) 2 + ( y + 1) 2 + ( z 2) 2 = 14 which describes the set of all points on a sphere of radius 14 and center C (3 , 1 , 2). 3. Write an equation for the set of all points ( x, y, z ) whose distance from (1 , 1 , 1) is the same as the distance from (2 , 0 , 3). (Simplify your equation). ( x 1) 2 + ( y 1) 2 + ( z 1) 2 = ( x 2) 2 + ( y 0) 2 + ( z 3) 2 or x 2 2 x + 1 + y 2 2 y + 1 + z 2 2 z + 1 = x 2 4 x + 4 + y 2 + z 2 6 z + 9 or x y + 2 z 5 = 0 (the equation of a plane). 4. Let −→ w = ( t, t, 2 ) , −→ v = ( 2 , t, 3 ) . Is there a value of t for which −→ w and −→ v are perpendicular ? Either find t or show carefully that there is no such t .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern