Let a, b, c be vectors of lengths 3, 4, 5 respectively and a be perpendicular to (b + c), b to (c + a) and c to (a + b), then the value of (a + b + c) is

For non-zero vectors a, b, c; |(a $$\times$$ b) . c| = |a| |b| |c| holds if and only if

If a and b are two vectors such that | a | = 1, | b | = 4 a . b = 2. If c = (2a $$\times$$ b) $$-$$ 3b, then angle between b and c

If $$a = - \widehat i + \widehat j + \widehat k$$ and $$b = 2\widehat i + \widehat k$$, then find z component of a vector r, which is coplanar with a and b, r . b = 0 and r . a = 7.