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.
1.9 a = -i + 5k, b = -3i + 2j + 2k, c = -2i - 4j + k; a) 3a, -4b, 2c; b) 7a, -3c; a) 2b, 3a; r) b, c; d) 7a, 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.
2.9 A (3, -2, 6), B (-6, -2, 3), C (1, 1, -4), D (4, 6, -7); 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.
3.9 F = (6, 5, -7), A (7, -6, 4), B (4, 9, -6)
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