Option 30 DHS 2.2

DHS - 2.2
№1.30. 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 two vectors are collinear or orthogonal; e) check whether the three vectors a (5; -6; -4) will be coplanar; b (4; 8; -7); c (0; 3; -4).
№2.30 The vertices of the pyramid are located at points A (–4; –2; –3); B (2; 5; 7); C (6; 3; –1); D (6; –4; 1). ....
№ 3.30. Three forces P are given (2; –1; –3); Q (3; 2; –1); R (–4; 1; 3); attached to point A (–1; 4; –2). 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; –1); b) the value of the moment of the resultant of these forces relative to point B.