Please help with this question

Question

Consider the rectangular box in R3 with edges given by the three vectors u = (2,0,0), v = (0, 2, 0) and w = (0, 0, 1) (with initial points equal to the origin). What is the angle between the diagonal of this rectangular box and the edge along the x−axis?

Answer 1

The question is asking for the angle of the diagonal to the x-axis <1, 0, 0>

Thus, use dot product

The vector of the diagonal coordinate is <2, 2, 1>

cos x = (<2, 2, 1> * <1, 0, 0>)/|<2, 2, 1>||<1, 0, 0>|

cos x = 2/3