21.9.1 - Orthogonal Vectors
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Practice Questions
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What are orthogonal vectors?
💡 Hint: Think about the angles formed between the vectors.
Define an orthonormal set.
💡 Hint: What additional condition must be met besides being orthogonal?
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Interactive Quizzes
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What is the dot product of two orthogonal vectors?
💡 Hint: What does their angle look like?
Is an orthonormal set always composed of orthogonal vectors?
💡 Hint: Consider both properties that define orthonormality.
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Challenge Problems
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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.
Prove that the vectors (1, 1) and (-1, 1) are orthogonal by calculating their dot product.
💡 Hint: Remember the formula for dot product calculation.
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