Question

a cube of edge length a=8.20 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.

Answer 1

Answer on Question #73166-Physics-Other

A cube of edge length $a = 8.20$ m sits with one corner at the origin of a 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.

Solution

(a)

$$a\hat{i} + a\hat{j} + a\hat{k}$$

(b)

$$- a\hat{i} + a\hat{j} + a\hat{k}$$

(c)

$$a\hat{i} - a\hat{j} + a\hat{k}$$

(d)

$$- a\hat{i} - a\hat{j} + a\hat{k}$$

(e)

$$\theta = \cos^{-1}\left(\frac{1}{\sqrt{3}}\right) \approx 54.7{}^\circ$$

(f)

$$d = a\sqrt{3}$$

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