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.
1.13 a = -5i + 2j - 2k, b = 7i - 5k, c = 2i + 3j - 2k; a) 2a, 4b, -5c; b) -3b, 11c; a) 8a, -6c; g) a, c; d) 8a, -3b, 11c.
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.
2.13 A (-4, -7, -3), B (-4, -5, 7), C (2, 3, 3), D (3, 2, 1); a) BCD; 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.
3.13 P = (9, 3, 4), Q (5, 6, -2), R (-4, -2, 7), A (-5, 4, -2), B (4, 6, -5)
Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)
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