Let a circle C in complex plane pass through the points $${z_1} = 3 + 4i$$, $${z_2} = 4 + 3i$$ and $${z_3} = 5i$$. If $$z( \ne {z_1})$$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then $$arg(z)$$ is equal to :

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is _____________.

Let $$\theta$$ be the angle between the vectors $$\overrightarrow a $$ and $$\overrightarrow b $$, where $$|\overrightarrow a | = 4,$$ $$|\overrightarrow b | = 3$$ and $$\theta \in \left( {{\pi \over 4},{\pi \over 3}} \right)$$. Then $${\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a + \overrightarrow b } \right)} \right|^2} + 4{\left( {\overrightarrow a \,.\,\overrightarrow b } \right)^2}$$ is equal to __________.

Let the abscissae of the two points P and Q be the roots of $$2{x^2} - rx + p = 0$$ and the ordinates of P and Q be the roots of $${x^2} - sx - q = 0$$. If the equation of the circle described on PQ as diameter is $$2({x^2} + {y^2}) - 11x - 14y - 22 = 0$$, then $$2r + s - 2q + p$$ is equal to __________.