Reshebnik Ryabushko. Solved IDZ 2.2, Option 7

1. Given vectors a, b and c. It is necessary: ​​a) calculate the mixed product of three vectors; b) find the module of the vector product; c) calculate the dot product of two vectors; d) check whether two vectors are collinear or orthogonal; e) check if three vectors are coplanar.
1.7 a = 4i - j + 3k, b = 2i + 3j - 5k, c = 7i + 2j + 4k; a) 7a, –4b, 2c; b) 3a, 5c; c) 2b, 4c; d) b, c; e) 7a, 2b, 5c.

2. The vertices of the pyramid are at points A, B, C and D. Calculate: a) the area of ​​the specified face; b) the area of ​​the section passing through the middle of the edge l and two vertices of the pyramid; c) the volume of the pyramid ABCD.
2.7 A (–4, 6, 3), B (3, –5, 1), C (2, 6, –4), D (2, 4, –5); a) ACD; b) l = AD, B and C

3. Force F is applied to point A. Calculate: a) work of force F in the case when the point of its application, moving in a straight line, moves to point B; b) the module of the moment of force F relative to point B.
3.7 F = (5, 4, 11), A (6, 1, –5), B (4, 2, –6)