IDZ 2.2 - Option 18. 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.
 1.18 a = 9i - 3j + k, b = 3i - 15j + 21k, c = i - 5j + 7k; a) 2a, -7b, 3c; b) -6a, 4c; a) 5b, 7a; r) b, c; d) 2a, -7b, 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.
 2.18 A (5, -4, 4), B (-4, -6, 5), C (3, 2, -7), D (6, 2, -9); a) ABD; 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.
 3.18 P = (-5, 8, 4), Q (6, -7, 3), R (3, 1, -5), A (2, -4, 7), B (0, 7, 4)