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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What are orthogonal vectors?
💡 Hint: Think about the angles formed between the vectors.
Question 2
Easy
Define an orthonormal set.
💡 Hint: What additional condition must be met besides being orthogonal?
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 is the dot product of two orthogonal vectors?
- 1
- 0
- Unknown
💡 Hint: What does their angle look like?
Question 2
Is an orthonormal set always composed of orthogonal vectors?
- True
- False
💡 Hint: Consider both properties that define orthonormality.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors v1 = (2, 3, 4) and v2 = (1, 2, -3), use the Gram-Schmidt process to create an orthonormal set.
💡 Hint: Follow the steps of normalization and projection carefully.
Question 2
Prove that the vectors (1, 1) and (-1, 1) are orthogonal by calculating their dot product.
💡 Hint: Remember the formula for dot product calculation.
Challenge and get performance evaluation