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Let 0 = (0,0,0), i = (1, 0, 0), j = (0, 1, 0), k = (0,0,1) be vectors in R³. Given in the figure below a cube with an edge length of 3 units. E F D 口 B У (a) Describe all points (x, y, z) in the cube. (b) Let P, Q, R, S, T, U be the centers of the faces AGFE, GBDF, DCEF, OAEC, OAGB, OBDC respectively, write the vectors OP, OQ, OR, OS, OT, OU, as a linear combination of i, j, and k. (c) Find the coordinates of the center point of the cube.

Let 0 = (0,0,0), i = (1, 0, 0), j = (0, 1, 0), k = (0,0,1) be vectors in R³. Given in the figure below a cube with an edge length of 3 units. E F D 口 B У (a) Describe all points (x, y, z) in the cube. (b) Let P, Q, R, S, T, U be the centers of the faces AGFE, GBDF, DCEF, OAEC, OAGB, OBDC respectively, write the vectors OP, OQ, OR, OS, OT, OU, as a linear combination of i, j, and k. (c) Find the coordinates of the center point of the cube.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 2CM: Take this test to review the material in Chapters 4and Chapters 5. After you are finished, check...
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Question
Let 0 = (0,0,0), i = (1, 0, 0), j = (0, 1, 0), k = (0,0,1) be vectors in R³. Given in the figure below a cube with an edge length of 3 units. E F D 口 B У (a) Describe all points (x, y, z) in the cube. (b) Let P, Q, R, S, T, U be the centers of the faces AGFE, GBDF, DCEF, OAEC, OAGB, OBDC respectively, write the vectors OP, OQ, OR, OS, OT, OU, as a linear combination of i, j, and k. (c) Find the coordinates of the center point of the cube.
Transcribed Image Text:Let 0 = (0,0,0), i = (1, 0, 0), j = (0, 1, 0), k = (0,0,1) be vectors in R³. Given in the figure below a cube with an edge length of 3 units. E F D 口 B У (a) Describe all points (x, y, z) in the cube. (b) Let P, Q, R, S, T, U be the centers of the faces AGFE, GBDF, DCEF, OAEC, OAGB, OBDC respectively, write the vectors OP, OQ, OR, OS, OT, OU, as a linear combination of i, j, and k. (c) Find the coordinates of the center point of the cube.
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