10 Referred to the origin \(O\), the points \(A , B\) and \(C\) have position vectors given by $$\overrightarrow { O A } = \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } , \quad \overrightarrow { O B } = 2 \mathbf { i } + 4 \mathbf { j } + \mathbf { k } \quad \text { and } \quad \overrightarrow { O C } = 3 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k }$$

1. Find the exact value of the cosine of angle \(B A C\).
2. Hence find the exact value of the area of triangle \(A B C\).
3. Find the equation of the plane which is parallel to the \(y\)-axis and contains the line through \(B\) and \(C\). Give your answer in the form \(a x + b y + c z = d\).