# IDZ 2.2 - Option 27. 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.
1.27 a = 3i - j + 5k, b = 2i - 4j + 6k, c = i - 2j + 3k; a) -3a, 4b, -5c; b) 6b, 3c; a) a, 4c; r) b, c; d) -3a, 4b, -c.

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.
2.27 A (-9, -7, 4), B (-4, 3, -1), C (5, -4, 2), D (3, 4, 4); a) BCD; b) l = CD, A and B

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.
3.27 P = (4, 2, 3), Q (-2, 5, 6), R (7, 3, -1), A (-3, -2, 5), B (9, -5, 4)