Parameterize the following objects: (a) The parallelogram with corners at (0,0,0), (0, 1, 1), (2, 2, 1), and (2,1,0). (Find a paramerization with rectangular domain (u, v) € [a, b] × [c, d].) (b) A "washer" shape in the xy-plane bounded by the inequalities 1< x² + y² ≤ 4. (Find a paramerization with rectangular domain (u, v) € [a, b] × [c, d].) (c) The curve where the cylinder x² + y² = 1 intersects the plane x + y + z = 1. (This is a curve, so find a parameterization with one variable t = [a, b].)

Parameterize the following objects: (a) The parallelogram with corners at (0,0,0), (0, 1, 1), (2, 2, 1), and (2,1,0). (Find a paramerization with rectangular domain (u, v) € [a, b] × [c, d].) (b) A "washer" shape in the xy-plane bounded by the inequalities 1< x² + y² ≤ 4. (Find a paramerization with rectangular domain (u, v) € [a, b] × [c, d].) (c) The curve where the cylinder x² + y² = 1 intersects the plane x + y + z = 1. (This is a curve, so find a parameterization with one variable t = [a, b].)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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