For each of the following shapes, draw their projections onto each of the xy-, xz-, and yz- planes, and specify which of these projections are one-to-one. ple) The half-cylinder given by the equation x² + y² = 1 with y ≥ 0 and 0 ≤ z < 1. The projections are drawn below: only the projection on the xz-plane is one-to-one. Y X X Y (a) The portion of the cone x² + y² = z² satisfying 0 ≤ z < 1. (b) The portion of the sphere x² + y² + z² = 1 in the first octant: where x, y, z are all nonnegative. (c) The portion of the surface z = sin y satisfying −1 ≤ x ≤ 1 and −π ≤ y ≤ π.
For each of the following shapes, draw their projections onto each of the xy-, xz-, and yz- planes, and specify which of these projections are one-to-one. ple) The half-cylinder given by the equation x² + y² = 1 with y ≥ 0 and 0 ≤ z < 1. The projections are drawn below: only the projection on the xz-plane is one-to-one. Y X X Y (a) The portion of the cone x² + y² = z² satisfying 0 ≤ z < 1. (b) The portion of the sphere x² + y² + z² = 1 in the first octant: where x, y, z are all nonnegative. (c) The portion of the surface z = sin y satisfying −1 ≤ x ≤ 1 and −π ≤ y ≤ π.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 19EQ
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Question
For each of the following shapes, draw their projections onto each of the xy-, xz-, and yzplanes, and specify which of these projections are one-to-one.
(a) The portion of the cone x^2 + y^2 = z^2 satisfying 0 ≤ z ≤ 1.
(b) The portion of the sphere x^2 + y^2 + z^2 = 1 in the first octant: where x, y, z are all nonnegative.
(c) The portion of the surface z = sin y satisfying −1 ≤ x ≤ 1 and −π ≤ y ≤ π.
Transcribed Image Text:For each of the following shapes, draw their projections onto each of the xy-, xz-, and yz-
planes, and specify which of these projections are one-to-one.
ple) The half-cylinder given by the equation x² + y² = 1 with y ≥ 0 and 0 ≤ z < 1.
The projections are drawn below: only the projection on the xz-plane is one-to-one.
Y
X
X
Y
(a) The portion of the cone x² + y² = z² satisfying 0 ≤ z < 1.
(b) The portion of the sphere x² + y² + z² = 1 in the first octant: where x, y, z are all
nonnegative.
(c) The portion of the surface z = sin y satisfying −1 ≤ x ≤ 1 and −π ≤ y ≤ π.
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