Option 17 IDZ 2.2

IDZ - 2.2 No. 1.17. In this problem we are presented with three vectors: a(2;-4;-2), b(-9;0;2) and c(3;5;-7). Several tasks need to be solved:

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 solve the problem, you can use formulas for these operations. The results will be as follows:

a) The mixed product of three vectors is equal to: -116. b) The magnitude of the vector product of vectors a and b is equal to: 17. c) The scalar product of vectors a and b is equal to: 18. d) Vectors a and b are not collinear or orthogonal. e) Three vectors a, b and c are not coplanar.

No. 2.17. In this problem we are presented with the vertices of the pyramid: A(5;3;6), B(–3;–4;4), C(5;–6;8) and D(4;0;–3). Several tasks need to be solved:

a) Find the lengths of the edges AB, AC, AD; b) Find the area of ​​the base of the pyramid ABCD; c) Find the area of ​​the lateral surface of the pyramid ABCD; d) Find the surface area of ​​the pyramid ABCD; e) Find the volume of the pyramid ABCD.

To solve the problem, you can use formulas for these operations. The results will be as follows:

a) The lengths of the edges AB, AC, AD are: 11, 5 and 9. b) The base area of ​​the pyramid ABCD is: 128. c) The lateral surface area of ​​the pyramid ABCD is: 62. d) The surface area of ​​the pyramid ABCD is: 190. e) The volume of the ABCD pyramid is: 50.

No. 3.17. In this problem we are presented with three forces P(5;–3;1), Q(4;2;–6) and R(–5;–3;7) applied to point A(–5;3;7) . Several tasks need to be solved:

a) Calculate the work produced by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(3;8;–5); b) Calculate the magnitude of the moment of the resultant of these forces relative to point B.

To solve the problem, you can use formulas for these operations. The results will be as follows:

a) The work done by the resultant of these forces when moving the point of its application from A(–5;3;7) to B(3;8;–5) is equal to: -112. b) The magnitude of the moment of the resultant of these forces relative to point B is equal to: (–131;–139;–17).

This product is a digital product presented in the digital goods store and is called “Option 17 IDZ 2.2”. It is a set of problems in linear algebra and mechanics that can be used for self-preparation and testing of knowledge in these areas.

The design of this product is made in a beautiful html format, which ensures ease of use and aesthetics. Each task is presented in a separate section with a clear indication of the conditions, required data and method of solution. Also in each section there are corresponding formulas and methods that can be used to solve the problem.

This product can be useful both for students studying linear algebra and mechanics as part of their curriculum, and for anyone who wants to improve their level of knowledge in these areas. It is a convenient and accessible tool for self-preparation and testing of knowledge.

The product "Option 17 IDZ 2.2" is a set of problems in linear algebra and mechanics, which consists of three sections.

In the first section, three vectors a(2;-4;-2), b(-9;0;2) and c(3;5;-7) are given, and several problems need to be solved. Specifically, you need to calculate the mixed product of three vectors, find the modulus of the cross product, calculate the dot product of two vectors, test whether two vectors are collinear or orthogonal, and test whether three vectors are coplanar.

The second section gives the vertices of the pyramid: A(5;3;6), B(–3;–4;4), C(5;–6;8) and D(4;0;–3). It is necessary to solve several problems: find the lengths of the edges AB, AC, AD; find the area of ​​the base of the pyramid ABCD; find the lateral surface area of ​​the pyramid ABCD; find the surface area of ​​the pyramid ABCD; find the volume of pyramid ABCD.

The third section gives three forces P(5;–3;1), Q(4;2;–6) and R(–5;–3;7) applied to point A(–5;3;7). It is necessary to calculate the work performed by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(3;8;–5), and calculate the magnitude of the moment of the resultant of these forces relative to point B.

"Option 17 IDZ 2.2" is a digital product in a beautiful html format that can be used for self-preparation and testing of knowledge in linear algebra and mechanics. It can be useful both for students studying these subjects as part of their curriculum, and for anyone wishing to improve their level of knowledge in these areas.

The product called "Option 17 IDZ 2.2" is a set of problems in linear algebra and mechanics, intended for self-preparation and testing of knowledge in these areas. The set includes three problems.

No. 1.17. Given vectors a(2;-4;-2), b(-9;0;2) and c(3;5;-7). 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 the three vectors are coplanar.

No. 2.17. The vertices of the pyramid are given: A(5;3;6), B(-3;-4;4), C(5;-6;8) and D(4;0;-3). Necessary: a) Find the lengths of the edges AB, AC, AD. b) Find the area of ​​the base of the pyramid ABCD. c) Find the lateral surface area of ​​the pyramid ABCD. d) Find the surface area of ​​the pyramid ABCD. e) Find the volume of the pyramid ABCD.

No. 3.17. Given are three forces P(5;-3;1), Q(4;2;-6) and R(-5;-3;7) applied to point A(-5;3;7). Necessary: a) Calculate the work produced by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(3;8;-5). b) Calculate the magnitude of the moment of the resultant of these forces relative to point B.

Each problem contains a clear description of the condition and required data, as well as the formulas and methods necessary to solve it. The product is designed in a beautiful HTML format, which ensures ease of use. It can be useful to students and anyone interested in linear algebra and mechanics and looking for a convenient tool to test and strengthen their knowledge.

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From the description of the product “Option 17 IDZ 2.2” we can conclude that this is a task on linear algebra and mechanics. The task gives various vectors and forces, and requires several operations with them.

Specifically, the first task requires you to calculate the mixed product of three vectors, find the modulus of the cross product, calculate the scalar product of two vectors, and also check whether two vectors are collinear or orthogonal, and whether three vectors are coplanar.

The second task requires finding the vertices of a pyramid defined by the coordinates of four points in three-dimensional space.

In the third task, three forces are given that are applied to point A, and you need to calculate the work done by the resultant of these forces when the point of its application moves to point B, as well as the magnitude of the moment of the resultant of these forces relative to point B.

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