Let a, b and c be three mutually perpendicular vectors each of unit magnitude. If

A = a + b + c, b = a $$-$$ b + c and C = a $$-$$ b $$-$$ c, then which one of the following is correct?

What is (a $$-$$ b) $$\times$$ (a + b) equal to ?

A spacecraft located at $$\widehat i + 2\widehat j + 3\widehat k$$ is subjected to a force $$\lambda \widehat k$$ by firing a rocket. The spacecraft is subjected to a moment of magnitude

In a triangle ABC, if taken in order, consider the following statements

1. AB + BC + CA = 0

2. AB + BC $$-$$ CA = 0

3. AB $$-$$ BC + CA = 0

4. BA $$-$$ BC + CA = 0

How many of the above statement are correct?