Векторы a и b образуют угол φ=π/2, и |a| = 3, |b| = 4. Вычислить:
1. |a x b|;
2. |(a+b) x (a-b)|;
3. |(a+2b) x (3a-2b)|.

Ответ:

1. |a x b| = |a| * |b| * sin(φ) = 3 * 4 * sin(π/2) = 12.

2. |(a+b) x (a-b)| = |a+b| * |a-b| * sin(φ) = (|a| + |b|) * (|a| - |b|) * sin(π/2) = (3 + 4) * (3 - 4) * sin(π/2) = -1.

3. |(a+2b) x (3a-2b)| = |a+2b| * |3a-2b| * sin(φ) = (|a| + 2|b|) * (3|a| - 2|b|) * sin(π/2) = (3 + 2*4) * (3*3 - 2*4) * sin(π/2) = 22.