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.
1.6 a = 3i - 2j + k, b = 2j - 3k, c = -3i + 2j - k; a) a, -3b, 2c; b) 5a, 3c; a) -2a, 4b; g) a, c; d) 5a, 4b, 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.
2.6 A (3, 4, 2), B (-2, 3, -5), C (4, 3, 6), D (6, -5, 3); a) ABD; 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.
3.6 F = (3, -5, 7), A (2, 3, -5), B (0, 4, 3)