In the figure, a cube of edge length a = 6.60 m 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. (a) Number i 3.30 (b) Number i 3.30 (c) Number i -3.30 (d) Number i 3.30 î + i 3.30 i -3.30 i 3.30 i 3.30 a + C.) (+ + .> + .> a i 3.30 i -3.30 i -3.30 i -3.30 k Units k Units k Units k Units m m m
In the figure, a cube of edge length a = 6.60 m 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. (a) Number i 3.30 (b) Number i 3.30 (c) Number i -3.30 (d) Number i 3.30 î + i 3.30 i -3.30 i 3.30 i 3.30 a + C.) (+ + .> + .> a i 3.30 i -3.30 i -3.30 i -3.30 k Units k Units k Units k Units m m m
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Transcribed Image Text:In the figure, a cube of edge length a = 6.60 m 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, O)? (e) Determine the angles
that the body diagonals make with the adjacent edges. (f) Determine the length of the body diagonals.
(a) Number i 3.30
(b) Number i 3.30
(c) Number i -3.30
(d) Number i 3.30
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i -3.30
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3.30
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a
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i
3.30
-3.30
-3.30
-3.30
k Units
Units m
k Units
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k Units
m
m
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We are given a cube. We are also given side or edge length of this cube. We are to draw body diagonal from given initial coordinates. We have to write this diagonal vector in component form. Where ever or whatever the diagonal is, the magnitude of its component along x, y, z directions will be equal to edge length of the cube. We just have to find directions of these components.
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