1. Given the vectors a, b, and c. 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; e) verify whether the three vectors are coplanar.
1.5 a = - 4i + 2j - k, b = 3i + 5j - 2k, c = j + 5k; a) a, 6b, 3c; b) 2b, a; a) a, -4c; g) a, b; d) a, 6b, 3c.
2. The top of the pyramid are located at points A, B, C and D. Calculate: a) the area of the said faces; b) cross-sectional area, passing through the middle of the rib l and two top of the pyramid; c) the volume of the pyramid ABCD.
2.5 A (-5, -3, -4), B (1, 4, 6), C (3, 2, -2), D (8, 2, 4); a) ACD; b) l = BC, A and D
3. The force F applied to point A. Calculate: a) operating force F when the point of its application, moving rectilinearly moves to point B; b) the time unit of the force F about the point B.
3.5 F = (4, 11, -6), A (3, 5, 1), B (4, -2, -3)