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.
1.7 a = 4i - j + 3k, b = 2i + 3j - 5k, c = 7i + 2j + 4k; a) 7a, -4b, 2c; b) 3a, 5c; a) 2b, 4c; r) b, c; d) 7a, 2b, 5c.
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.
2.7 A (-4, 6, 3), B (3, -5, 1), C (2, 6, -4), D (2, 4, -5); a) ACD; b) l = AD, B 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.
3.7 F = (5, 4, 11), A (6, 1, -5), B (4, 2, -6)