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