Option 20 IDZ 2.2

IDZ - 2.2 No. 1.20

Vector data:

• a(-9;4;-5)
• b(1;-2;4)
• c(-5;10;-20)

Necessary:

1. Calculate the mixed product of three vectors
2. Find the cross product modulus
3. Calculate the dot product of two vectors
4. Check if two vectors are collinear or orthogonal
5. Check if three vectors are coplanar

№2.20

The tops of the pyramid are located at the points:

• A(7;–1;–2)
• B(1;7;8)
• C(3;7;9)
• D(–3;–5;2)

№3.20

Three forces are given:

• P(3;–4;2)
• Q(2;3;–5 )
• R(–3;–2;4)

Attached to point A(5;3;–7).

Calculate:

1. The work done by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(4;–1;–4)
2. The magnitude of the resultant moment of these forces relative to point B

Task No. 1.20: Given vectors a(-9;4;-5), b(1;-2;4) and c(-5;10;-20). 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 the three vectors are coplanar.

Task No. 2.20: The vertices of the pyramid are located at points A(7;-1;-2), B(1;7;8), C(3;7;9) and D(-3;-5;2).

Task No. 3.20: Given three forces P(3;-4;2), Q(2;3;-5) and R(-3;-2;4) applied to point A(5;3;-7) . Calculate: a) the work produced by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(4;-1;-4); b) the magnitude of the moment of the resultant of these forces relative to point B.

Description of the digital product

Option 20 IDZ 2.2

This digital product is a set of tasks for IDZ 2.2 in linear algebra, including tasks No. 1.20, No. 2.20 and No. 3.20.

Problem #1.20 is a set of computational problems involving vectors, such as calculating the mixed product of three vectors, the modulus of the vector product, the scalar product of two vectors, and testing for collinearity, orthogonality, and coplanarity of vectors.

Task No. 2.20 contains the task of determining the vertices of a pyramid according to given coordinates.

Task No. 3.20 includes tasks on calculating the work produced by the resultant of three forces when they move, as well as determining the magnitude of the moment of the resultant of these forces relative to a given point.

The set of tasks IDZ 2.2 is intended for students studying linear algebra and solving problems in vector algebra.

By purchasing this product, you receive a high-quality and useful tool for studying and practical application of linear algebra material.

This product is a set of tasks for IDZ 2.2 in linear algebra, which includes three tasks.

Assignment 1.20 consists of computational problems involving vectors. It is necessary 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 vectors for this task are given as follows: a(-9;4;-5), b(1;-2;4) and c(-5;10;-20).

Task No. 2.20 contains the task of determining the vertices of a pyramid according to given coordinates. The vertices of the pyramid are defined as follows: A(7;–1;–2), B(1;7;8), C(3;7;9) and D(–3;–5;2).

Task No. 3.20 includes tasks on calculating the work produced by the resultant of three forces when they move, as well as determining the magnitude of the moment of the resultant of these forces relative to a given point. To solve this problem, you need to know three forces applied to point A(5;3;–7): P(3;–4;2), Q(2;3;–5) and R(–3;–2; 4). It is required to calculate the work done by the resultant of these forces when the point of its application moves linearly to point B(4;–1;–4), and also to determine the magnitude of the moment of the resultant of these forces relative to point B.

The set of tasks IDZ 2.2 is intended for students studying linear algebra and solving problems in vector algebra. By purchasing this product, you receive a high-quality and useful tool for studying and practical application of linear algebra material.

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IDZ 2.2 No. 1.20 is a task on calculating various quantities associated with vectors. Three vectors are given: a(-9;4;-5), b(1;-2;4) and c(-5;10;-20).

a) It is necessary to 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. 2.20. The task gives the coordinates of the vertices of the pyramid: A(7;–1;–2), B(1;7;8), C(3;7;9) and D(–3;–5;2).

No. 3.20. The task gives three forces applied to point A(5;3;–7): P(3;–4;2), Q(2;3;–5) and R(–3;–2;4). It is necessary to calculate the work produced by the resultant of these forces when the point of its application, moving rectilinearly, moves to point B(4;–1;–4), as well as the magnitude of the moment of the resultant of these forces relative to point B.

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