Question #b4645

1 Answer
Cesareo R.
Nov 1, 2016

#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#

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