Verify the Pythagorean Theorem for the vectors u and v. u = (-3, 2, 4), v = (2, 3, 0) STEP 1: Compute u · v. Are u and v orthogonal? O Yes No

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Verify the Pythagorean Theorem for the vectors **u** and **v**.

**u** = \((-3, 2, 4)\),  **v** = \((2, 3, 0)\)

**STEP 1**: Compute \( \mathbf{u} \cdot \mathbf{v} \).

\[ \]

Are **u** and **v** orthogonal?

- [x] Yes
- [ ] No

**STEP 2**: Compute \( \|\mathbf{u}\|^2 \) and \( \|\mathbf{v}\|^2 \).

\(\|\mathbf{u}\|^2 = \)

\[ \]

\(\|\mathbf{v}\|^2 = \)

\[ \]

**STEP 3**: Compute \( \mathbf{u} + \mathbf{v} \) and \( \|\mathbf{u} + \mathbf{v}\|^2 \).

\(\mathbf{u} + \mathbf{v} = \)

\[ \]

\(\|\mathbf{u} + \mathbf{v}\|^2 = \)

\[ \]

**STEP 4**: Is the statement \(\|\mathbf{u} + \mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2\) true?

- [x] Yes
- [ ] No
Transcribed Image Text:Verify the Pythagorean Theorem for the vectors **u** and **v**. **u** = \((-3, 2, 4)\), **v** = \((2, 3, 0)\) **STEP 1**: Compute \( \mathbf{u} \cdot \mathbf{v} \). \[ \] Are **u** and **v** orthogonal? - [x] Yes - [ ] No **STEP 2**: Compute \( \|\mathbf{u}\|^2 \) and \( \|\mathbf{v}\|^2 \). \(\|\mathbf{u}\|^2 = \) \[ \] \(\|\mathbf{v}\|^2 = \) \[ \] **STEP 3**: Compute \( \mathbf{u} + \mathbf{v} \) and \( \|\mathbf{u} + \mathbf{v}\|^2 \). \(\mathbf{u} + \mathbf{v} = \) \[ \] \(\|\mathbf{u} + \mathbf{v}\|^2 = \) \[ \] **STEP 4**: Is the statement \(\|\mathbf{u} + \mathbf{v}\|^2 = \|\mathbf{u}\|^2 + \|\mathbf{v}\|^2\) true? - [x] Yes - [ ] No
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