If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b.

If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i + \widehat j + 2\widehat k$$, then find $$[a\,b\,c]$$.

If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is

If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k$$, then a vector perpendicular to a and in the plane containing b and c is