Solution IDZ Ryabushko 2.2 - Option 20

Section: Chapter 2. Vector algebra
Topic: Vector and mixed media
Description: Calculate vector and mixed products, check collinearity, orthogonality and coplanarity. Application to finding areas, volumes, work of force and moment of force.

Tasks:
1. Given vectors a, b and c. It is necessary: a) calculate the mixed product of three vectors; b) find the modulus of the vector product; c) calculate the scalar product of two vectors; d) check whether two vectors are collinear or orthogonal; e) check whether three vectors are coplanar.
2. The vertices of the pyramid are at points A, B, C and D. Calculate: a) the area of the specified face; b) the cross-sectional area passing through the midpoint of edge l and two vertices of the pyramid; c) the volume of the pyramid ABCD.
3. Force F is applied to point A. Calculate: a) the work of force F when its point of application, moving in a straight line, moves to point B; b) the modulus of the moment of force F relative to point B.

The complete solution includes:
• Complete solution to all 3 tasks of the option
• Detailed explanations for each step
• All formulas and calculations
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