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.
1.1 a = 2i - 3j + k, b = j + 4k, c = 5i + 2j - 3k; a) a, 3b, c; b) 3a, 2c; a) b, -4c; g) a, c; d) a, 2b, 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.
2.1 A (3, 4, 5), B (1, 2, 1), C (-2, -3, 6), D (3, -6, -3); a) ACD; b) l = AB, C 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.
3.1 F = (5, 3, 9), A (3, 4, -6), B (2, 6, 5)