IDZ 2.2 - Option 14. Decisions Ryabushko AP

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.
 1.14 a = -4i - 6j + 2k, b = 2i + 3j - k, c = -i + 5j - 3k; a) 5a, 7b, 2c; b) -4b, 11a; a) 3a, -7c; g) a, b; d) 3a, 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.
 2.14 A (-4, -5, -3), B (3, 1, 2), C (5, 7, -6), D (6, 1, 5); a) ACD; b) l = BC, A and D

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