1.
2а={-8;4;8}, b/2={sqrt(2)/2;-sqrt(2)/2;0}
|2a|=sqrt(64+16+64)=sqrt(128+16)=12
|b/2|=sqrt(1/2+1/2+0)=1
cos(2a;b/2)=(-4sqrt(2)-2sqrt(2))/12=(-6sqrt(2))/12= -sqrt(2)/2
∠(2a;b/2)=arccos(-sqrt(2)/2)=3pi/4
2.
BA={-8;4;4}
3.
n=a+2b={2;0;1}+{2;-4;6}={4;-4;7}
|n|=sqrt(16+16+49)=sqrt(32+49)=sqrt(81)=9
4.
{4;19}={2m;3m}+{3n;-2n}
Составляем систему:
2m+3n=4
3m-2n=19
m=(4-3n)/2
(3/2)(4-3n)-2n=19
m=(4-3n)/2
6-4,5n-2n=19
m=(4-3n)/2
6,5n= -13
n= -2
m=5