Explanation

The magnitude of a vector is its length.

For vector ⟨x, y⟩:
|v| = √(x² + y²)

This comes from the Pythagorean Theorem.

Example:
v = ⟨3, 4⟩
|v| = √(3² + 4²) = √25 = 5

Quiz

1. What does |v| represent?

2. Write the magnitude formula.

3. Find the magnitude of ⟨6, 8⟩.

4. Is magnitude ever negative?

5. What theorem is used here?

Answer Key

1. Length of the vector

2. √(x² + y²)

3. 10

4. No

5. Pythagorean Theorem