2) a transformation im 3d space takes (a,b,c) to (x,y,z) where

(x)=(0 0 1)(a)

(y)=(1 0 0)(b)

(z)=(0 1 0)(c)

this transformation leaves distance between 2 points the same and leaves unaltered the points of the line x=y=z.

Assuming the transformation is a rotation about a line,find the angle of rotation.

the answer is 120 degrees but i cant find a decent way of explaining why. Im guessing the line of rotation is x=y=z and as lengths stay the same when i look at (1,0,0) which goes to (0,1,0) i get 2 equilateral triangles,one either side of the line.