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MATH213: Homework 1 - Finding Equations of Planes and Sketching Surfaces, Assignments of Mathematics

Colorado School of MinesMathematics

The homework assignment for math213: sections h and j, due on august 27, 2008. The assignment includes finding the equation of a plane given three points and sketching various surfaces. The surfaces to be sketched include parabolic and quadratic functions in cartesian coordinates.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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MATH213: Sections H and J Homework 1 Due: August 27, 2008
1. (10 points) Given the points P= (p1, p2, p3), Q= (q1, q2, q3), and R= (r1, r2, r3), find the equation of the
plane containing P,Q, and R.
2. Identify and sketch the following surfaces:
(a) (2 points)
x=p1โˆ’y2
โˆ’z2
(b) (1 point)
y= 2 โˆ’x
(c) (2 points)
z=โˆš3px2+y2
(d) (3 points)
y= 3 โˆ’x2
โˆ’z2
(e) (2 points)
x2+y2= 5

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MATH213: Sections H and J Homework 1 Due: August 27, 2008

  1. (10 points) Given the points P = (p 1 , p 2 , p 3 ), Q = (q 1 , q 2 , q 3 ), and R = (r 1 , r 2 , r 3 ), find the equation of the plane containing P , Q, and R.
  2. Identify and sketch the following surfaces:

(a) (2 points) x =

1 โˆ’ y^2 โˆ’ z^2

(b) (1 point) y = 2 โˆ’ x

(c) (2 points) z =

x^2 + y^2

(d) (3 points) y = 3 โˆ’ x^2 โˆ’ z^2

(e) (2 points) x^2 + y^2 = 5