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.
1.30 a = 5i - 6j - 4k, b = 4i + 8j - 7k, c = 3j - 4k; a) 5a, 3b, -4c; b) 4b, a; a) 7a, -2c; g) a, b; d) 5a, 4b, -2c.
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.
2.30 A (-4, -2, -3), B (2, 5, 7), C (6, 3, -1), D (6, -4, 1); a) ACD; 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.
3.30 P = (2, -1, -3), Q (3, 2, -1), R (-4, 1, 3), A (-1, 4, -2), B (2, 3, -1)