#x+y+z+3 =0# is the equation of a plane in #RR^3#. This plane can be generated by a linear form with the structure
#Pi->p = p_0+lambda_1 vec v_1+lambda_2 vec v_2#
The given plane is given with the structure
#Pi_0-> << p-p_0,vec v >> = 0#
with
#p = (x,y,z)#
#p_0=(-1,-1,-1)# and
#vec v = (1,1,1)#
Here #Pi# and #Pi_0# are equivalent if #vec v = vec v_1 xx vec v_2# because then
#Pi_0-> << p_0+lambda_1 vec v_1+lambda_2 vec v_2-p_0, vec v >> = 0#
The affine space #Pi# is generated by the linear combinations of two independent vectors #{vec v_1, vec v_2} in RR^3# with the property:
#vec v_1 ne 0, vec v_2 ne 0, << vec v_1, vec v >> = << vec v_2, vec v >>=0#
