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