What is the angle between the diagonals of a cube?

Question

Hint: set up a unit cube with one corner at the origin

Answer 1

4 answers so far and not one of them right!

Those diagonals lie on a rectangle through opposite edges of the cube. The rectangle's long edge is root2. Doing the trig, the crossing angle of the diagonals is 180 - 2(arctan(rt2)) = 70.528 deg

Answer 2

The angle between the diagonals of the cube has to be 90 degrees

Answer 3

The angle between the diagonals of a cube must be 45 degrees. This angle should measures 45 degrees over the three X,Y,and Z axis. The x,y and z Axis form 90 degrees within each . The line the bisects these three Axis should form 45 degrees.

Answer 4

Consider the diagonal from (0, 0, 0) to (1, 1, 1) and (1, 0, 0) to (0, 1, 1). These correspond to the vectors <1, 1, 1> and <-1, 1, 1>, respectively. The angle between vectors a and b is given by arccos (a·b/(||a||*||b||)). ||a||=||b||=√3, so we have:
arccos (<1, 1, 1>·<-1, 1, 1>/3)
arccos ((-1+1+1)/3)
arccos (1/3)
≈ 70.528779º

Which agrees with steve's answer.

Answer 5

draw a cube and dash in the diagonals and you will see they are at right angles to each other. Don't just wait for someone to give you the answer see it for yourself.

Answer 6

i see steve's answer but i believe cube means a 6 square sides so it would be 90 degrees

Answer 7

90 degrees