IDZ 2.2 - Option 25. 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.
 1.25 a = -3i - j - 5k, b = 2i - 4j + 8k, c = 3i + 7j - k; a) 2a, -b, 3c; b) -9a, 4c; a) 5b, -6c; r) b, c; d) 2a, 5b, -6c.

 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.
 2.25 A (-8, 2, 7), B (3, -5, 9), C (2, 4, -6), D (4, 6, -5); a) ACD; b) l = AD, B 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.
 3.25 P = (5, 5, -6), Q = (7, -6, 6), R = (-4, 3, 4), A (-9, 4, 7), B (8, 1, 7 )