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Math 233 - Spring 08 Exam One: Solutions and Questions, Exams of Analytical Geometry and Calculus

University of Wisconsin (UW) - MilwaukeeAnalytical Geometry and Calculus

The spring 2008 exam for math 233, which covers various topics in vector calculus. The exam includes questions on finding the center and radius of a sphere, finding component form of vectors, scalar and vector projections, finding vectors orthogonal to planes, and equations of lines and planes. Students are required to show all work and clearly label answers.

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

koofers-user-wrk
koofers-user-wrk 🇺🇸

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Math 233 - Spring 08 - Exam One
SHOW ALL WORK.
Work must be correct, clear, and organized. Answers must be
clearly and correctly labeled.
1) (6 points) Show that the equation represents a sphere, and find its center
and radius. Clearly label the center and radius.
x2+y2+z2=x+y+z
1
pf3
pf4
pf5
pf8

Partial preview of the text

Download Math 233 - Spring 08 Exam One: Solutions and Questions and more Exams Analytical Geometry and Calculus in PDF only on Docsity!

Math 233 - Spring 08 - Exam One SHOW ALL WORK. Work must be correct, clear, and organized. Answers must be clearly and correctly labeled.

  1. (6 points) Show that the equation represents a sphere, and find its center and radius. Clearly label the center and radius.

x^2 + y^2 + z^2 = x + y + z

  1. (6 points) If ~v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |~v| = 4, find ~v in component form.
  1. (6 points) If ~a = 〈 3 , 0 , − 1 〉, find a vector ~b such that comp~a~b = 2.
  • 5 (6 points) Show that ~ 0 × ~a = ~0 = ~a × ~0 for any vector ~a in V
  1. (6 points) Find an equation of the plane. The plane that passes through the point (6, 0 , −2) and contains the line x = 4 − 2 t, y = 3 + 5t, z = 7 + 4t.
  1. (6 points) Find parametric equations for the line through the point (0, 1 , 2) that is parallel to the plane x + y + z = 2 and perpendicular to the line x = 1 + t, y = 1 − t, z = 2t.