a cube of edge length a sits with one corner at the origin of an xyz coordinate system. A body diagonal is a line that extends from one corner to another through the center. In unit-vector notation, what is the body diagonal that extends from the corner at (a) coordinates (0, 0, 0), (b) coordinates (a, 0, 0), (c) coordinates (0, a, 0), and (d) coordinates (a, a, 0)? (e) Determine the angles that the body diagonals make with the adjacent edges. (f) Determine the length of the body diagonals in terms of a.

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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a cube of edge
length a sits with one corner at the origin
of an xyz coordinate system. A
body diagonal is a line that extends
from one corner to another through
the center. In unit-vector notation,
what is the body diagonal that extends
from the corner at (a) coordinates (0,
0, 0), (b) coordinates (a, 0, 0), (c) coordinates
(0, a, 0), and (d) coordinates (a, a, 0)? (e) Determine the angles that the body diagonals make with the adjacent edges.
(f) Determine the length of the body diagonals in terms of a.

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