1.1.40 Vector Algebra

Condition: Given the coordinates of the vertices of the pyramid \( A(4,2,3,) ; \quad B(-5 ;-4 ; 2) ; \quad C(5 ; 7 ;-4) \quad \) and \( D(6,4,-7) \). Find a) the volume of the pyramid; b) the area of ​​the section passing through the middle of the edge \(A D\) and the vertices \(B\) and \(C\); c) cosine of the angle between the edges \( D A \) and \( D C \).