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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define orthogonal vectors.
💡 Hint: Think about their geometric representation.
Question 2
Easy
What condition must be met for vectors to be orthonormal?
💡 Hint: Recall the definition of unit length.
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?
- Their dot product is one.
- Their dot product is zero.
- They have the same direction.
💡 Hint: Think about how two vectors' directions relate in space.
Question 2
True or False: All orthonormal vectors are orthogonal.
- True
- False
💡 Hint: Recall the definition of orthonormal sets.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors A = (2, 3, 6) and B = (1, -1, 2), are they orthogonal? Verify your answer.
💡 Hint: Remember to calculate the dot product correctly.
Question 2
Find a new orthonormal basis for the vectors in R² given by (4, 3) and (1, 1) using the Gram-Schmidt process.
💡 Hint: Follow the Gram-Schmidt steps methodically.
Challenge and get performance evaluation