Determine which set of vectors is not orthogonal. v = (-10,0), w = (0,5) v = (0,1), w = (0,1) O O v = (10,10), w = (−1,1) Ov=(9,-3), w = (−2, −6)
Determine which set of vectors is not orthogonal. v = (-10,0), w = (0,5) v = (0,1), w = (0,1) O O v = (10,10), w = (−1,1) Ov=(9,-3), w = (−2, −6)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Which Set of Vectors is Not Orthogonal?
In this problem, you are given multiple pairs of vectors. Your task is to determine which pair of vectors is **not** orthogonal.
Recall that two vectors \( \mathbf{v} \) and \( \mathbf{w} \) are orthogonal if their dot product is zero. The dot product of \(\mathbf{v} = (v_1, v_2)\) and \(\mathbf{w} = (w_1, w_2)\) is calculated as:
\[ v_1 \cdot w_1 + v_2 \cdot w_2 \]
Now, examine each pair of vectors below:
1. **Pair 1:**
\[
\mathbf{v} = \langle -10, 0 \rangle, \quad \mathbf{w} = \langle 0, 5 \rangle
\]
**Dot Product Calculation:**
\[ (-10) \cdot 0 + 0 \cdot 5 = 0 + 0 = 0 \]
2. **Pair 2:**
\[
\mathbf{v} = \langle 0, 1 \rangle, \quad \mathbf{w} = \langle 0, 1 \rangle
\]
**Dot Product Calculation:**
\[ 0 \cdot 0 + 1 \cdot 1 = 0 + 1 = 1 \]
3. **Pair 3:**
\[
\mathbf{v} = \langle 10, 10 \rangle, \quad \mathbf{w} = \langle -1, 1 \rangle
\]
**Dot Product Calculation:**
\[ 10 \cdot (-1) + 10 \cdot 1 = -10 + 10 = 0 \]
4. **Pair 4:**
\[
\mathbf{v} = \langle 9, -3 \rangle, \quad \mathbf{w} = \langle -2, -6 \rangle
\]
**Dot Product Calculation:**
\[ 9 \cdot (-2) + (-3) \cdot (-6) = -18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f02248d-9b04-4bf9-ba6b-18c74681389d%2F525c0a63-2ba3-4805-a846-8f3621d88e10%2Fpfu00x8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Which Set of Vectors is Not Orthogonal?
In this problem, you are given multiple pairs of vectors. Your task is to determine which pair of vectors is **not** orthogonal.
Recall that two vectors \( \mathbf{v} \) and \( \mathbf{w} \) are orthogonal if their dot product is zero. The dot product of \(\mathbf{v} = (v_1, v_2)\) and \(\mathbf{w} = (w_1, w_2)\) is calculated as:
\[ v_1 \cdot w_1 + v_2 \cdot w_2 \]
Now, examine each pair of vectors below:
1. **Pair 1:**
\[
\mathbf{v} = \langle -10, 0 \rangle, \quad \mathbf{w} = \langle 0, 5 \rangle
\]
**Dot Product Calculation:**
\[ (-10) \cdot 0 + 0 \cdot 5 = 0 + 0 = 0 \]
2. **Pair 2:**
\[
\mathbf{v} = \langle 0, 1 \rangle, \quad \mathbf{w} = \langle 0, 1 \rangle
\]
**Dot Product Calculation:**
\[ 0 \cdot 0 + 1 \cdot 1 = 0 + 1 = 1 \]
3. **Pair 3:**
\[
\mathbf{v} = \langle 10, 10 \rangle, \quad \mathbf{w} = \langle -1, 1 \rangle
\]
**Dot Product Calculation:**
\[ 10 \cdot (-1) + 10 \cdot 1 = -10 + 10 = 0 \]
4. **Pair 4:**
\[
\mathbf{v} = \langle 9, -3 \rangle, \quad \mathbf{w} = \langle -2, -6 \rangle
\]
**Dot Product Calculation:**
\[ 9 \cdot (-2) + (-3) \cdot (-6) = -18
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