Question

решите, пожалуйста))))

Answer 1

1) 2a = (8; -16; 4)
1/3*b = (-2; 3; 1)
c(1; 0; -5)
2a - 1/3*b + c = (8+2+1; -16-3+0; 4-1-5) = (11; -19; -2)

2) |a|=2; |b|=4; (a;b)=60°
a*b = |a|*|b|*cos(a;b) = 2*4*1/2 = 4

3) a(-3; 0; 4); b(1; -2; 2)
|a| = √((-3)^2+0^2+4^2) = √25 = 5
|b| = √(1^2+(-2)^2+2^2) = √9 = 3
a*b = (-3)*1+0*(-2)+4*2 = -3+8 = 5
cos(a;b) = a*b/(|a|*|b|) = 5/(5*3) = 1/3

4) A(11; -2; -9); B(2; 6; -4); C(14; 2; -10).
|AB| = √((11-2)^2+(-2-6)^2+(-9+4)^2) = √(9^2+8^2+5^2) =
= √(81+64+25) = √170
|AC| = √((11-14)^2+(-2-2)^2+(-9+10)^2) = √(3^2+4^2+1^2) =
= √(9+16+1) = √26
|BC| = √((2-14)^2+(6-2)^2+(-4+10)^2) = √(12^2+4^2+6^2) =
= √(144+16+36) = √196 = 14
P(ABC) = √170 + √26 + 14