**Title:** Understanding Vector Magnitude and OperationsIn this exercise, we aim to find the magnitudes of given vectors and perform specific operations.**Vectors:**- \( \mathbf{u} = (1, -3) \)- \( \mathbf{v} = (-4, -4) \)**Tasks:**Calculate the following:- \( |\mathbf{u}| \)- \( |\mathbf{v}| \)- \( |2\mathbf{u}| \)- \( \frac{1}{2}|\mathbf{v}| \)- \( |\mathbf{u} + \mathbf{v}| \)- \( |\mathbf{u} - \mathbf{v}| \)- \( ||\mathbf{u}| - |\mathbf{v}|| \)**Results:**- \( |\mathbf{u}| = \sqrt{10} \) ✔️- \( |\mathbf{v}| = 4\sqrt{2} \) ✔️- \( |2\mathbf{u}| = 6.32456 \) ❌- \( \frac{1}{2}|\mathbf{v}| = 2\sqrt{2} \) ✔️- \( |\mathbf{u} + \mathbf{v}| = \sqrt{2(5+4)} \) ❌- \( |\mathbf{u} - \mathbf{v}| = \sqrt{2(5-4)} \) ❌- \( ||\mathbf{u}| - |\mathbf{v}|| = 2\sqrt{(5-4)} \) ✔️**Explanation of the Mistakes:**- The error in calculating \( |2\mathbf{u}| \) likely arises from a miscalculation. Ensure you double the components first and then find the magnitude.- The mistakes in \( |\mathbf{u} + \mathbf{v}| \) and \( |\mathbf{u} - \mathbf{v}| \) show potential errors in summing or subtracting vectors and finding the magnitude thereafter.This practice highlights common mistakes in handling vector operations and reinforces accurate computation.

Answered: Image /qna-images/answer/b039be68-701f-4b5d-82b2-9ffd2a3c5f57.jpg

Find lul, Ivl, 12ul, · 121.14 lu+vl, lu- vl, and lul - lvl. u = (1, -3), v = (-4,-4) lul=√10 |v1 = 4√2 12u1= 6.32456 x = 2√2 lu+v1 = ✓ √2 (√5 + 4) * √2 (√5-4) x lu-vl = lul- lvl = √2 (√5 4)

Find lul, Ivl, 12ul, · 121.14 lu+vl, lu- vl, and lul - lvl. u = (1, -3), v = (-4,-4) lul=√10 |v1 = 4√2 12u1= 6.32456 x = 2√2 lu+v1 = ✓ √2 (√5 + 4) * √2 (√5-4) x lu-vl = lul- lvl = √2 (√5 4)

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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