- With respect to a fixed origin \(O\), the line \(l\) has equation
$$( \mathbf { r } - ( 12 \mathbf { i } + 16 \mathbf { j } - 8 \mathbf { k } ) ) \times ( 9 \mathbf { i } + 6 \mathbf { j } + 2 \mathbf { k } ) = \mathbf { 0 }$$
The point \(A\) lies on \(l\) such that the direction cosines of \(\overrightarrow { O A }\) with respect to the \(\mathbf { i } , \mathbf { j }\) and \(\mathbf { k }\) axes are \(\frac { 3 } { 7 } , \beta\) and \(\gamma\).
Determine the coordinates of the point \(A\).