9 Relative to the origin \(O\), the position vectors of the points \(A , B\) and \(C\) are given by $$\overrightarrow { \mathrm { OA } } = 5 \mathbf { i } - 2 \mathbf { j } + \mathbf { k } , \quad \overrightarrow { \mathrm { OB } } = 8 \mathbf { i } + 2 \mathbf { j } - 6 \mathbf { k } \quad \text { and } \quad \overrightarrow { \mathrm { OC } } = 3 \mathbf { i } + 4 \mathbf { j } - 7 \mathbf { k }$$

1. Show that \(O A B C\) is a rectangle.
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   \includegraphics[max width=\textwidth, alt={}, center]{446573d3-73b1-482a-a3f6-1abddfdd90d0-14_68_1575_648_322}
   \includegraphics[max width=\textwidth, alt={}]{446573d3-73b1-482a-a3f6-1abddfdd90d0-14_70_1573_737_324} ....................................................................................................................................... .........................................................................................................................................
2. Use a scalar product to find the acute angle between the diagonals of \(O A B C\).