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?

If a and b are vectors such that | a | = 2, | b | = 7 and a $$\times$$ b = $$3\widehat i + 2\widehat j + 6\widehat k$$, then what is the acute angle between a and b?

Let p and q be the position vectors of the points P and Q respectively with respect to origin O. The points R and S divide PQ internally and externally respectively in the ratio 2 : 3. If OR and OS are perpendicular, then which one of the following is correct?