Option 23 DHS 2.2

DHS - 2.2
No. 1.23. 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 (4; -6; -2); b (-2; 3; 1); c (3; -5; 7).
№2.23. The vertices of the pyramid are at points A (–6; –3; –5); B (5; 1; 7); C (3; 5; –1); D (4; –2; 9). .........
№3.23. Three forces P are given (9; –4; 4); Q (–4; 6; –3); R (3; 4; 2); attached to point A (5; –4; 3). Calculate a) the work produced by the resultant of these forces; when the point of its application, moving in a straight line, moves to the point B (4; –5; 9); b) the value of the moment of the resultant of these forces relative to point B.