# Math Help - Unit Cube

1. ## Unit Cube

By locating a unit cube in an appropriate position in the 3-dimensional rectangular coordinate system, determine the acute angle formed by the two diagonals of the cube.

2. pretty sure this is correct ...

let one diagonal go from the origin to the point (1,1,1)

its direction vector is a = <1,1,1>

let the other diagonal go from (1,0,0) to (0,1,1)

its direction vector is b = <-1,1,1>

the dot product of the two direction vectors = 1

|a| = |b| = $\sqrt{3}$

$3\cos{\theta} = 1$

$\cos{\theta} = \frac{1}{3}$

$\theta \approx 70.5^{\circ}$