IDZ Ryabushko 2.2 Option 2

No. 1. For a given set of vectors, it is necessary to perform the following actions: 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: a(3;4;1);b(1;-2;7);c(3;-6;2).

No. 2. There are pyramid vertices A(–7;–5;6), B(–2;5;–3), C(3;–2;4) and D(1;2;2).

No. 3. Force F(–3;1;–9) is applied at point A(6;–3;5). It is necessary: ​​a) calculate the work of force F in the case when the point of its application, moving rectilinearly, moves to point B(9;5;–7); b) calculate the modulus of the moment of force F relative to point B.

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"IDZ Ryabushko 2.2 Option 2" is a digital product intended for students and schoolchildren who study mathematics and want to successfully complete their homework. The product contains solutions to problems in mathematics, including algebra, geometry, trigonometry and calculus. The solutions are carried out by qualified specialists and checked for correctness. The product has a beautiful HTML design, which makes its use convenient and enjoyable. A convenient structure allows you to quickly find the desired section and task.

In addition, the product contains solutions to problems that can be useful not only for completing homework, but also for preparing for exams. In particular, the product contains solutions to problems in vector algebra No. 1, problems in geometry No. 2 and problems in mechanics No. 3.

In vector algebra problems #1, you need to perform various operations with vectors, such as calculating the mixed product of three vectors, finding the modulus of the vector product, dot product, and checking for collinearity and coplanarity of vectors.

In geometry problems No. 2, it is necessary to solve the problem of constructing a pyramid and calculating its volume, as well as finding the length of an edge and the angles between the edges.

Problems in mechanics No. 3 are related to the calculation of the work of a force and the modulus of the moment of force relative to the point of application. Problems can be useful when studying physics or mechanics.

The product "IDZ Ryabushko 2.2 Option 2" can be useful for students and schoolchildren who study mathematics and want to successfully complete their homework, as well as for those who are preparing for exams in mathematics, physics or mechanics.

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IDZ Ryabushko 2.2 Option 2 is a linear algebra task consisting of three numbers.

No. 1. In this task you need to perform several operations on vectors: 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 the three vectors are coplanar.

To complete the task, three vectors are given: a(3;4;1), b(1;-2;7), c(3;-6;2).

No. 2. In this task you need to find the volume of a pyramid whose vertices are at points A(–7;–5;6), B(–2;5;–3), C(3;–2;4) and D(1;2 ;2).

No. 3. In this task, it is necessary to calculate the work done by the force F(–3;1;–9) applied to point A(6;–3;5) in two cases: a) when moving the point of application of force to point B(9;5;–7) in a straight line; b) find the modulus of the moment of force F relative to point B.

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