In the drawing, a cube of edge length a = 7.90 m sitswith one corner at the orig
ID: 1760539 • Letter: I
Question
In the drawing, a cube of edge length a = 7.90 m sitswith one corner at the origin of an xyz coordinate system.A body diagonal is a line that extends from one corner to anotherthrough the center. Find the angle between each pair of bodydiagonals. This is the last question I have on my homework and I'm notreally sure how to figure it out. Can anyone help. Max pointsawarded for correct answer and detailed process. Thanks. In the drawing, a cube of edge length a = 7.90 m sitswith one corner at the origin of an xyz coordinate system.A body diagonal is a line that extends from one corner to anotherthrough the center. Find the angle between each pair of bodydiagonals. This is the last question I have on my homework and I'm notreally sure how to figure it out. Can anyone help. Max pointsawarded for correct answer and detailed process. Thanks.Explanation / Answer
Let O(0, 0, 0), A(a, a, a), the vector OA = (a, a,a), magnitude OA = 3 a B(a, a, 0), C(0, 0, a),the vector CB = (a, a, -a),magnitude CB = 3 a OA . CB = OA*CB*cos a2 = 3 a * 3 a * cos cos = 1/3 = 70.5o