Option 2 DHS 2.2

DHS - 2.2
№1.2. 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 are coplanar: a (3; 4; 1); b (1; -2; 7); c (3; -6; 2).
№2.2. The vertices of the pyramid are at points A (–7; –5; 6); B (–2; 5; –3); C (3; –2; 4); D (1; 2; 2). Calculate: a) the area of ​​the face ACD; b) the cross-sectional area passing through the middle of the rib BC and the top of the pyramid A and D; c) the volume of the pyramid.
№ 3.2. The force F (–3; 1; –9) is applied to the point A (6; –3; 5). Calculate a) the work force F in the case; when the point of its application; moving straight; moves to point B (9; 5; –7); b) the modulus of momentum of force F relative to point B.