1. A) B(0; 6; -2)

2. OA = √(x² + y² + z²) = √(25 + 1 + 4) = √30

3. a(6; -2; -3), b(6; 6; 3)

1) |a| = √(36 + 4 + 9) = √49 = 7 (A)

2) |b| = √(36 + 36 + 9) = √81 = 9 (B)

3) |b - a| = |(0; 8; 6)| = √(0 + 64 + 36) = √100 = 10 (Г)

4) a·b = 6·6 - 2·6 - 3·3 = 36 - 12 - 9 = 15 (Д)

4. x₁ = 2x₀ - x₂ = -10 - 3 = -13;  

y₁ = 2y₀ - y₂ = 6 - 1 = 5;  

z₁ = 2z₀ - z₂ = 20 - 14 = 6

М(-13; 5; 6)

5. a·b = 0;

-4·2 + n·3 + 4·5 = 0;

-8 + 3n + 20 = 0;

3n = -12;

n = -4.

6. A(1; -3; -1), B(4; -2; 2), C(9; 5; -7)

x₀ = (x₁ + x₂)/2 = (1 + 9)/2 = 10/2 = 5

y₀ = (y₁ + y₂)/2 = (-3 + 5)/2 = 2/2 = 1

z₀ = (z₁ + z₂)/2 = (-1 - 7)/2 = -8/2 = -4

N(5; 1; -4)

BN = √(5² + 1² + 4²) = √(25 + 1 + 16) = √42

7. k = BD₁

BD₁ = √(a² + b² + c²) = √(BC² + BA² + BB₁²) = √(36 + 4 + 16) = 2√14