Option 14 DHS 2.2

Option 14 DHS 2.2

№1.14. Given the vector. It is necessary: ​​a) to calculate the mixed product of three vectors, b) to 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 are coplanar: a (-4; -6; 2); b (2; 3; -1); c (1; -5; 3).
No. 2.14. The vertices of the pyramid are at points A (–4; –5; –3); B (3; 1; 2); C (5; 7; –6); D (6; –1; 5). .....
No. 3.14. Three forces are given P (5; –2; 3); Q (4; 5; –3); R (–1; –3; 6); attached to point A (7; 1; –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 the point B (2; –3; –6); b) the magnitude of the moment of the resultant of these forces relative to point B.