IDZ Ryabushko 2.2 Variant 23

Number 1 are given the vector. It is necessary: ​​a) to calculate the mixed product of 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 are coplanar. a (4; -6; -2); b (-2; 3; 1); c (3; -5; 7).

No. 2 The vertices of the pyramid are located at points A (–6; –3; –5); B (5; 1; 7); C (3; 5; –1); D (4; –2; 9) ...

No. 3 Given three forces P (9; –4; 4); Q (–4; 6; –3); R (3; 4; 2); applied to point A (5; –4; 3). Calculate a) the work produced by the resultant of these forces; when the point of its application, moving rectilinearly, moves to point B (4; –5; 9); b) the magnitude of the moment of the resultant of these forces relative to point B.