In a cube of edge length a sits with one corncr 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 , what is the body diagonal that extends from the corner at (a) corrdianates (0,0,0), (b) corrdinates (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 boedy diagonals in terms of a.

In a cube of edge length a sits with one corncr at the origin of an xy

1.	In a cube of edge length a sits with one corncr 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 , what is the body diagonal that extends from the corner at (a) corrdianates (0,0,0), (b) corrdinates (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 boedy diagonals in terms of a.
Answer» SOLUTION :`(a) a HATI + a HATJ + ahatk, (b) - ahati + ahatj + ahatk(C ) a hati - a hatj +ahatk , (e) 54.7^(@)(F) a sqrt3`

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