Option 27 DHS 2.2

DHS - 2.2
No. 1.27. 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; 6); c (1; -2; 3);
No. 2.27. The vertices of the pyramid are at points A (–9; –7; 4); B (–4; 3; –1); C (5; –4; 2); D (3; 4; 4) ......
№ 3.27. Three forces P are given (4; –2; 3); Q (–2; 5; 6); R (7; 3; –1); attached to point A (–3; –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 the point B (9; –5; 4); b) size
the moment of the resultant of these forces relative to point B.