Question
Find, to the nearest tenth of a degree, the
angle formed by the two main diagonals of a
cube that connect consecutive vertices of the
lower base to the opposite consecutive
vertices of the upper base, as illustrated at
right.
angle formed by the two main diagonals of a
cube that connect consecutive vertices of the
lower base to the opposite consecutive
vertices of the upper base, as illustrated at
right.
Answers
Steve
can't see your diagram, but consider the vectors representing the diagonals. If it's a unit cube, they might be joining
(0,0,0) and (1,1,1) = <1,1,1>
(1,1,0) and (0,0,1) = <-1,-1,1>
(1,0,0) and (0,1,1) = <-1,1,1>
...
Now just take the dot product of the two diagonals you are interested in and
u•v = 3cosθ
(0,0,0) and (1,1,1) = <1,1,1>
(1,1,0) and (0,0,1) = <-1,-1,1>
(1,0,0) and (0,1,1) = <-1,1,1>
...
Now just take the dot product of the two diagonals you are interested in and
u•v = 3cosθ