Option 25 DHS 2.2

DHS - 2.2
№1.25. Given the vector. It is necessary: ​​a) to calculate the mixed product of the three vectors; b) find the module of the vector product; c) calculate the scalar product of two vectors; d) check whether the two vectors are collinear or orthogonal; e) check whether the three vectors a (-3; -1; -5) will be coplanar; b (2; -4; 8); c (3; 7; -1)
№2.25. The vertices of the pyramid are at points A (–8; 2; 7); B (3; –5; 9); C (2; 4; –6); D (4; 6; –5) .......
№3.25. Three forces P are given (5; 5; –6); Q (7; –6; 6); R (–4; 3; 4); attached to point A (–9; 4; 7). Calculate a) the work produced by the resultant of these forces; when the point of its application, moving straight, moves to the point B (8; –1; 7); b) the value of the moment of the resultant of these forces relative to point B.