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