Найдем векторное произведение a × b:
a × b = (2; -2; 0) × (3; -4; 5) = (2(-4) - (-2)3; -(25 - 03); 23 - (-2)5) = (-8 + 6; -10; 6 + 10) = (-2; -10; 16)

Найдем угол между векторами b и a:
cos(angle) = (a b) / (|a| |b|) = ((32) + (-4)(-2) + 50) / (sqrt(3^2 + (-4)^2 + 5^2) sqrt(2^2 + (-2)^2 + 0^2)) = (6 + 8) / (sqrt(35) sqrt(8)) = 14 / (5 2 sqrt(7)) = 14 / (10 sqrt(7)) = 7 / 5sqrt(7)

Найдем длины векторов |a|, |b| и |c|:
|a| = sqrt(2^2 + (-2)^2 + 0^2) = sqrt(4 + 4) = sqrt(8) = 2sqrt(2)
|b| = sqrt(3^2 + (-4)^2 + 5^2) = sqrt(9 + 16 + 25) = sqrt(50) = 5sqrt(2)
|c| = sqrt(0^2 + 2^2 + 4^2) = sqrt(0 + 4 + 16) = sqrt(20) = 2sqrt(5)

Ответ:
a × b = (-2; -10; 16)
Угол(b; a) ≈ 7 / 5sqrt(7)
|a| = 2sqrt(2)
|b| = 5sqrt(2)
|c| = 2sqrt(5)