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.
1.17 a = 2i - 4j - 2k, b = -9i + 2k, c = 3i + 5j - 7k; a) 7a, 5b, -c; b) -5a, 4b; a) 3b, -8c; g) a, c; d) 7a, 5b, -c.
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.
2.17 A (5, 3, 6), B (-3, -4, 4), C (5, -6, 8), D (4, 0, -3); a) BCD; 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.
3.17 P = (5, 3, 1), Q (4, 2, -6), R (-5, -3, 7), A (-5, 3, 7), B (3, 8, - 5)