7 Points \(A ( 2,2,5 ) , B ( 1 , - 1 , - 4 ) , C ( 3,3,10 )\) and \(D ( 8,6,3 )\) are the vertices of a pyramid with a triangular base.
- Calculate the lengths \(A B\) and \(A C\), and the angle \(B A C\).
- Show that \(\overrightarrow { A D }\) is perpendicular to both \(\overrightarrow { A B }\) and \(\overrightarrow { A C }\).
- Calculate the volume of the pyramid \(A B C D\).
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[The volume of the pyramid is \(V = \frac { 1 } { 3 } \times\) base area × perpendicular height.]