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?

What is the moment about the point $$\widehat i + 2\widehat j - \widehat k$$ of a force represented by $$3\widehat i + \widehat k$$ acting through the point $$2\widehat i - \widehat j + 3\widehat k$$ ?

If a + 2b + 3c = 0 and a $$\times$$ b + b $$\times$$ c + c $$\times$$ a = $$\lambda$$ (b $$\times$$ c), then what is the value of $$\lambda$$ ?