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.
1.11 a = 5i - 3j + 4k, b = 2i - 4j - 2k, c = 3i + 5j - 7k; a) a, -4b, 2c; b) -2b, 4c; a) -3a, 6c; r) b, c; d) a, -2b, 6c.
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.
2.11 A (3, -5, -2), B (-4, 2, 3), C (1, 5, 7), D (-2, -4, 5); a) ACD; b) l = BD, A and C
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.
3.11 F = (4, 7, -3), A (5, -4, 2), B (8, 5, 4)