Question

In a unit cube. Find The angle between the diagonals of two faces of the cube through the same vertex?

Answer 1

Vector representations of the diagonals joining the points (0,0,0) to (1,1,1) and (1,0,0) to (011) are <1,1,1> and <1,1,1>.Let θ be the angle between the two vectors.$<1,1,1>\times <-1,1,1>=-1+1+1=1$

This gives $cos\theta =\frac{1}{3}$ .