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.
1.2 a = 3i + 4j + k, b = i - 2j + 7k, c = 3i - 6j + 21k; a) 5a, 2b, c; b) 4b, 2c; a) a, c; r) b, c; d) 2a, -3b, c.
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.
2.2 A (-7, -5, 6), B (-2, 5, -3), C (3, 2, 4), D (1, 2, 2); a) BCD; b) l = CD, A and B
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.
3.2 F = (-3, 1, -9), A (6, 3, 5), B (9, 5, -7)