The vertices \( B \) and \( C \) of a triangle \( ABC \) lie on the line \( \dfrac{x}{1} = \dfrac{1 - y}{-2} = \dfrac{z - 2}{3} \). The coordinates of \( A \) and \( B \) are \( (1, 6, 3) \) and \( (4, 9, \alpha) \) respectively and \( C \) is at a distance of \( 10 \) units from \( B \). The area (in sq. units) of \( \triangle ABC \) is:
