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.
1.21 a = 2i - 7j + 5k, b = -i + 2j - 6k, c = 3i + 2j - 4k; a) -3a, 6b, -c; b) 5b, 3c; a) 7a, -4b; r) b, c; d) 7a, -4b, 3c.
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.
2.21 A (5, 2, 7), B (7, -6, -9), C (-7, -6, 3), D (1, -5, 2); a) ABD; b) l = AB, C 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.
3.21 P = (4, -2, -5), Q (5, 1, -3), R (-6, 2, 5), A (-3, 2, -6), B (4, 5, -3)