Option 22 DHS 2.2

DHS - 2.2
№1.22. 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 will be coplanar. a (7; -4; -5); b (1; -11; 3); c (5; 5; 3).
№2.22. The vertices of the pyramid are at points A (–2; –5; –1); B (–6; –7; 9); C (4; –5; 1); D (2; 1; 4). ..........
№3.22. Three forces P are given (7; 3; –4); Q (9; –4; 2); R (–6; 1; 4); attached to point A (–7; 2; 5). Calculate a) the work produced by the resultant of these forces; when the point of its application, moving in a straight line, moves to point B (4; –2; 11); b) the value of the moment of the resultant of these forces relative to point B.