IDZ 2.2 - Option 24. Decisions Ryabushko AP

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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.
1.24 a = 3i - j + 2k, b = -i + 5j - 4k, c = 6i - 2j + 4k; a) 4a, -7b, -2c; b) 6a, -4c; a) -2a, 5b; g) a, c; d) 6a, -7b, -2c.

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.
2.24 A (7, 4, 2), B (-5, 3, -9), C (1, -5, 3), D (7, -9, 1); a) ABD; b) l = BD, A and C

3. Given three powers P, Q, R, applied to point A. Calculate: a) work done by the resultant of these forces, when the point of its application, moving rectilinearly moves to point B; b) the amount of time the resultant of these forces about point B.
3.24 P = (6, -4, 5), Q (-4, 7, 8), R (5, 1, -3), A (-5, -4, 2), B (7, -3, 6)