КС
Ксюша Суперская
если m перпендикулярно n, то их скалярное произведение =0, т. е.
(m,n) = 0,
(m,n) = (A*a+17b, 3a-b) = 3*(A*a+17b,a) - (A*a+17b,b) =
= 3*( A*(a,a) + 17*(b,a) ) - ( A*(a,b) + 17*(b,b) = [ (b,a)=(a,b) ]=
= 3A*(a,a) + (a,b)*(17*3 - A) + (-17)*(b,b)= #
(a,a) = |a|^2 = 4,
(b,b) = |b|^2 = 25,
(a,b) = |a|*|b|*cos(120 град) = 2*5*(-1/2) = -5.
# = 3A*4 + (-5)*(51-A) - 17*(25) = 0,
12A - 5*51 + 5A - 17*25 = 0,
17A = 5*(51+17*5) = 5*(51 + 50 + 35) = 5*(136),
A = 5*136/17 = 5*8 = 40.