Ryabushko A.P. IDZ 2.2 option 2

DHS - 2.2
№1.2. Given the vector. It is necessary to: a) calculate the mixed product of three vectors; b) Find the unit vector product; c) to calculate the inner product of two vectors; g) check whether collinear or orthogonal two vectors; d) check whether coplanar three vectors: a (3; 4; 1); b (1, -2, 7); c (3, -6 and 2).
№2.2. The tops of the pyramids are located 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) cross-sectional area, passing through the middle of the ribs and the top of the pyramid BC A and D; c) the volume of the pyramid.
№3.2. The strength of F (-3; 1 - 9) is applied to point A (6; -3; 5). Calculate a) operation in the event of force F; when its point of application; moving in a straight line; moves to point B (9, 5, -7); b) the time unit of the force F about the point B.