## Problem StatementFind the component form of **u + v** given the lengths of **u** and **v** and the angles that **u** and **v** make with the positive x-axis.### Given Data:- $ ||\mathbf{u}|| = 3 $, $\theta_u = 5^\circ$- $ ||\mathbf{v}|| = 1 $, $\theta_v = 3^\circ$### Component Form Calculation:To find the component form of the vector sum **u + v**, we first convert each vector from its magnitude and angle to its component form.For vector **u**:- $ \mathbf{u}_x = ||\mathbf{u}|| \cos(\theta_u) $- $ \mathbf{u}_y = ||\mathbf{u}|| \sin(\theta_u) $For vector **v**:- $ \mathbf{v}_x = ||\mathbf{v}|| \cos(\theta_v) $- $ \mathbf{v}_y = ||\mathbf{v}|| \sin(\theta_v) $Then, we sum the corresponding components of **u** and **v** to get **u + v**:- $ (\mathbf{u} + \mathbf{v})_x = \mathbf{u}_x + \mathbf{v}_x $- $ (\mathbf{u} + \mathbf{v})_y = \mathbf{u}_y + \mathbf{v}_y $Combining these, we get the component form of **u + v**:\[ \mathbf{u} + \mathbf{v} = \left( (\mathbf{u} + \mathbf{v})_x, \, (\mathbf{u} + \mathbf{v})_y \right) \]

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Answered: Find the component form of u + v given…

Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ||u|| = 3, O, = 5 ||v|| = 1, 0, = 3 u + v =

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 8CLT

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Question

## Problem Statement

Find the component form of **u + v** given the lengths of **u** and **v** and the angles that **u** and **v** make with the positive x-axis.

### Given Data:
- $ ||\mathbf{u}|| = 3 $, $\theta_u = 5^\circ$
- $ ||\mathbf{v}|| = 1 $, $\theta_v = 3^\circ$

### Component Form Calculation:
To find the component form of the vector sum **u + v**, we first convert each vector from its magnitude and angle to its component form.

For vector **u**:
- $ \mathbf{u}_x = ||\mathbf{u}|| \cos(\theta_u) $
- $ \mathbf{u}_y = ||\mathbf{u}|| \sin(\theta_u) $

For vector **v**:
- $ \mathbf{v}_x = ||\mathbf{v}|| \cos(\theta_v) $
- $ \mathbf{v}_y = ||\mathbf{v}|| \sin(\theta_v) $

Then, we sum the corresponding components of **u** and **v** to get **u + v**:
- $ (\mathbf{u} + \mathbf{v})_x = \mathbf{u}_x + \mathbf{v}_x $
- $ (\mathbf{u} + \mathbf{v})_y = \mathbf{u}_y + \mathbf{v}_y $

Combining these, we get the component form of **u + v**:

\[ \mathbf{u} + \mathbf{v} = \left( (\mathbf{u} + \mathbf{v})_x, \, (\mathbf{u} + \mathbf{v})_y \right) \]

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