Question

Question #b4645

Answer 1

`pi/3`

Explanation:

Another representation for

`Pi_1->2x - y + z = 3` and
`Pi_2->x + y + 2z =1`

is

`Pi_1-><< vec n_1, p-p_1 >> =0` and
`Pi_2-><< vec n_2, p-p_2 >> =0`

with

`p = (x,y,z)`
`vec n_1=(2,-1,1), p_1 = (0,0,3)` and
`vec n_2=(1,1,2), p_2= (0,0,1/2)`

where `vec n_1, vec n_2` are the normal vectors to `Pi_1` and `Pi_2` respectively. So the dihedrical angle `alpha` between `Pi_1` and `Pi_2` is obtained by doing

`<< vec n_1, vec n_2 >> = norm(vec n_1) norm(vec n_2) cosalpha`

so

`alpha = arccos((<< vec n_1, vec n_2 >>)/(norm(vec n_1) norm(vec n_2) )) = pi/3`