Explore and Discuss 1 Imagine that you are facing the front of a classroom whose rectangular walls meet at right angles. Suppose that the point of intersection of the floor, front wall, and left-side wall is the origin of a three-dimensional coordinate system in which every point in thc room has nonnegative coordinates. Then the plane z = 0 (or,equivalently. the. xy plane) can be described as “the floor” and the plane z = 2 can be described as “the plane parallel to, but 2 units above, the floor.” Give similar descriptions of the following planes: (A) x = 0 (B) x = 3 (C) y = 0 (D) y = 4 (E) x = −1
Explore and Discuss 1 Imagine that you are facing the front of a classroom whose rectangular walls meet at right angles. Suppose that the point of intersection of the floor, front wall, and left-side wall is the origin of a three-dimensional coordinate system in which every point in thc room has nonnegative coordinates. Then the plane z = 0 (or,equivalently. the. xy plane) can be described as “the floor” and the plane z = 2 can be described as “the plane parallel to, but 2 units above, the floor.” Give similar descriptions of the following planes: (A) x = 0 (B) x = 3 (C) y = 0 (D) y = 4 (E) x = −1
Solution Summary: The author describes the plane x=0, yz -plane, and floor.
Imagine that you are facing the front of a classroom whose rectangular walls meet at right angles. Suppose that the point of intersection of the floor, front wall, and left-side wall is the origin of a three-dimensional coordinate system in which every point in thc room has nonnegative coordinates. Then the plane z = 0 (or,equivalently. the.xy plane) can be described as “the floor” and the plane z = 2 can be described as “the plane parallel to, but 2 units above, the floor.” Give similar descriptions of the following planes:
(A) x = 0
(B) x = 3
(C) y = 0
(D) y = 4
(E) x = −1
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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