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Find u · v, where 0 is the angle between u and v. ||u|| = 100, ||v|| = 230, 0 6

Find u · v, where 0 is the angle between u and v. ||u|| = 100, ||v|| = 230, 0 6

Calculus: Early Transcendentals
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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**Problem Statement:** Find \(\mathbf{u} \cdot \mathbf{v}\), where \(\theta\) is the angle between \(\mathbf{u}\) and \(\mathbf{v}\). **Given:** - \(\|\mathbf{u}\| = 100\) - \(\|\mathbf{v}\| = 230\) - \(\theta = \frac{\pi}{6}\) **To Do:** Calculate the dot product \(\mathbf{u} \cdot \mathbf{v}\). **Explanation:** The dot product \(\mathbf{u} \cdot \mathbf{v}\) is given by the formula: \[ \mathbf{u} \cdot \mathbf{v} = \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta) \] **Box:** Empty - to fill with the calculated result.
Transcribed Image Text:**Problem Statement:** Find \(\mathbf{u} \cdot \mathbf{v}\), where \(\theta\) is the angle between \(\mathbf{u}\) and \(\mathbf{v}\). **Given:** - \(\|\mathbf{u}\| = 100\) - \(\|\mathbf{v}\| = 230\) - \(\theta = \frac{\pi}{6}\) **To Do:** Calculate the dot product \(\mathbf{u} \cdot \mathbf{v}\). **Explanation:** The dot product \(\mathbf{u} \cdot \mathbf{v}\) is given by the formula: \[ \mathbf{u} \cdot \mathbf{v} = \|\mathbf{u}\| \|\mathbf{v}\| \cos(\theta) \] **Box:** Empty - to fill with the calculated result.
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