9 With respect to the origin \(O\), the vertices of a triangle \(A B C\) have position vectors $$\overrightarrow { O A } = 2 \mathbf { i } + 5 \mathbf { k } , \quad \overrightarrow { O B } = 3 \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } \quad \text { and } \quad \overrightarrow { O C } = \mathbf { i } + \mathbf { j } + \mathbf { k }$$

1. Using a scalar product, show that angle \(A B C\) is a right angle.
2. Show that triangle \(A B C\) is isosceles.
3. Find the exact length of the perpendicular from \(O\) to the line through \(B\) and \(C\).