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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 angle with respect to each other.
Question 2
Easy
What conditions must a set of vectors meet to be considered orthonormal?
💡 Hint: Recall the properties of orthogonality and 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 defines two vectors as orthogonal?
- Their lengths are equal
- Their inner product equals zero
- They lie in the same direction
💡 Hint: Think about what it means for two lines to meet.
Question 2
True or False: An orthonormal set can contain vectors that are not of unit length.
- True
- False
💡 Hint: Consider the criteria for orthonormal sets.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two vectors u = (2, -1) and v = (-0.5, 1) in R^2, determine if they are orthogonal.
💡 Hint: Find the inner product to check their orthogonality.
Question 2
Assert whether the following set of vectors forms an orthonormal set: A = { (1,0), (0,1), (1,1)/√2, (1,-1)/√2 }.
💡 Hint: Evaluate each vector's length and their pairwise inner products.
Challenge and get performance evaluation