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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define orthogonality in your own words.
💡 Hint: Think about the geometric interpretation of two lines.
Question 2
Easy
Are the vectors [1, 2] and [-2, 1] orthogonal? Justify your answer.
💡 Hint: Calculate the dot product to check.
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 does it mean for two vectors to be orthogonal?
- They have the same direction
- Their dot product is zero
- They are linearly dependent
💡 Hint: Think about the geometric relationship between the vectors.
Question 2
Is it true or false? Orthogonal vectors cannot be linearly dependent.
- True
- False
💡 Hint: Consider the properties of independence!
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors A = [3, -4], B = [4, 2], and C = [0, 0], determine if they are linearly independent. Provide a justification.
💡 Hint: Calculate dot products and assess the coefficients.
Question 2
In a mechanical system, explain how having linearly dependent vectors can impact the solution to structural analysis problems.
💡 Hint: Consider the equations in equilibrium and how they relate to the forces in the structure.
Challenge and get performance evaluation