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.
1.20 a = -9i + 4j - 5k, b = i - 2j + 4k, c = -5i + 10j - 20k; a) -2a, 7b, 5c; b) -6b, 7c; a) 9a, 4c; 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.
2.20 A (7, -1, -2), B (1, 7, 8), C (3, 7, 9), D (-3, -5, 2); a) ACD; 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.
3.20 P = (3, -4, 2), Q (2, 3, -5), R (-3, -2, 4), A (5, 3, -7), B (4, -1, -4)