Practice Transformation of vector components - 3 | 4. Stress matrix | Solid Mechanics
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3 - Transformation of vector components

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a rotation matrix and its role in vector transformation.

💡 Hint: Think about how angles affect the orientation of the vector.

Question 2

Easy

What do we multiply vector components by to transform their representation?

💡 Hint: What version of the rotation matrix are we using?

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What must you do to transform vector components from one coordinate system to another?

  • Multiply by the rotation matrix
  • Multiply by the transpose of the rotation matrix
  • Add both systems' components

💡 Hint: Which matrix is applied to the components?

Question 2

Is it true that the vector itself remains unchanged during transformation?

  • True
  • False

💡 Hint: Think about how you express the same vector in different systems.

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Challenge Problems

Push your limits with challenges.

Question 1

A force vector is represented as (10 N, 0 N) along the x-axis. If the system is rotated 90 degrees counterclockwise, what will its new components be?

💡 Hint: Think about what a 90-degree rotation does to the orientation of the axes!

Question 2

You have a vector expressed as (2, -3) in one coordinate system. The second coordinate system is rotated 60 degrees clockwise. What are the new coordinates?

💡 Hint: Remember to use co-functions for the angles when computing trigonometric values.

Challenge and get performance evaluation