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