IDZ 2.2 - Option 29. 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.
 1.29 a = -9i + 4k, b = 2i - 4j + 6k, c = 3i - 6j + 9k; a) 3a, -5b, -4c; b) 6b, 2c; a) -2a, 8c; r) b, c; d) 3a, 6b, -4c.

 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.
 2.29 A (4, 2, 3), B (-5, -4, 2), C (5, 7, -4), D (6, 4, -7); a) ABD; 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.
 3.29 P = (3, 2, 4), Q (-4, 4, -3), R (3, 4, 2), A (1, -4, 3), B (4, 0, -2 )