Practice Orthogonal Vectors - 21.9.1 | 21. Linear Algebra | Mathematics (Civil Engineering -1)
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Orthogonal Vectors

21.9.1 - Orthogonal Vectors

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Practice Questions

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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?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

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Challenge 1 Hard

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.

Challenge 2 Hard

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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