IDZ Ryabushko 2.2 Option 11

No. 1 Given vectors a(5;-3;4), b(2;-4;-2) and c(3;5;-7). The following steps must be performed: 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 Given the vertices of the pyramid: A(3;-5;-2), B(-4;2;3), C(1;5;7) and D(-2;-4;5).

No. 3 Force F(4;7;-3) is applied to point A(5;-4;2). It is necessary to perform the following actions: a) Calculate the work of force F in the case when the point of its application, moving rectilinearly, moves to point B(8;5;-4). b) Calculate the modulus of the moment of force F relative to point B.

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We guarantee that each task in this IPD is unique and is not repeated in other versions. Moreover, all tasks are developed by experienced teachers and meet modern requirements of educational standards.

IPD includes tasks for calculating mixed and vector products, scalar products, checking collinearity, orthogonality and coplanarity of vectors.

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IDZ Ryabushko 2.2 Option 11 is a digital product intended for completing individual homework in mathematics on the topic “Vectors”. This IPD contains tasks related to vector operations, such as the mixed product of three vectors, the modulus of the vector product, the scalar product of two vectors, checking collinearity, orthogonality and coplanarity of vectors.

In addition, the IPD contains tasks related to calculating the work of a force and the modulus of the moment of force. The tasks use specific numerical values ​​of vectors and points, for example, vectors a(5;-3;4), b(2;-4;-2) and c(3;5;-7), vertices of the pyramid A(3; -5;-2), B(-4;2;3), C(1;5;7) and D(-2;-4;5), as well as strength F(4;7;-3), applied to point A(5;-4;2).

When you purchase Ryabushko IDZ 2.2 Option 11, you will receive a unique task that was developed by experienced teachers and meets modern educational standards. This digital product will help you improve your math skills and complete your academic assignments successfully.

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IDZ Ryabushko 2.2 Option 11 is a set of problems in linear algebra and mechanics, which includes the following tasks:

1. Three vectors are given:

a = (5;-3;4) b = (2;-4;-2) c = (3;5;-7)

The following steps are required:

a) Calculate the mixed product of three vectors. b) Find the modulus of the vector product of two vectors. 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.

1. The vertices of the pyramid are given:

A(3;–5;–2) B(–4;2;3) C(1;5;7) D(–2;–4;5)

You need to find the described pyramid.

1. Given is the force F(4;7;–3) applied to point A(5;–4;2).

The following steps are required: a) Calculate the work done by force F in the case when the point of its application, moving rectilinearly, moves to point B(8;5;–4). b) Calculate the modulus of the moment of force F relative to point B.

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