IDZ 2.2 - Option 28. 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.
 1.28 a = 4i - 5j - 4k, b = 5i - j, c = 2i + 4j - 3k; a) a, 7b, -2c; b) -5a, 4b; a) 8c, -3a; g) a, c; d) -3a, 4b, 8c.

 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.
 2.28 A (3, 5, 3), B (-3, 2, 8), C (-3, -2, 6), D (7, 8, -2); a) ACD; 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.
 3.28 P = (7, 3, -4), Q (3, -2, 2), R (-5, 4, 3), A (-5, 0, 4), B (4, 3, 5 )