Q45E Find the angle between each of t... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 1: Q45E (page 1)

Find the angle between each of thesepairs of vectors:
(a) $\overset{鈫�}{A} = - 2.00 \hat{i} + 6.00 \hat{j} and \overset{鈫�}{B} = 2.00 \hat{i} - 3.00 \hat{j}$
(b) $\overset{鈫�}{A} = 3.00 \hat{i} + 5.00 \hat{j} and \overset{鈫�}{B} = 10.00 \hat{i} + 6.00 \hat{j}$
(c) $\overset{鈫�}{A} = - 4.00 \hat{i} + 2.00 \hat{j} and \overset{鈫�}{B} = 7.00 \hat{i} + 14.00 \hat{j}$

Short Answer

Expert verified

The angles are $\cos^{- 1} (\frac{- 22}{\sqrt{40} \sqrt{13}}), \cos^{- 1} (\frac{60}{\sqrt{34} \sqrt{136}})$ and $0$ .

Step by step solution

Given data

$\overset{鈫�}{A} = - 2.00 \hat{i} + 6.00 \hat{j}$ and $\overset{鈫�}{B} = 2.00 \hat{i} - 3.00 \hat{j}$

$\overset{鈫�}{A} = 3.00 \hat{i} + 5.00 \hat{j}$ and $\overset{鈫�}{B} = 10.00 \hat{i} + 6.00 \hat{j}$

$\overset{鈫�}{A} = - 4.00 \hat{i} + 2.00 \hat{j}$ and $\overset{鈫�}{B} = 7.00 \hat{i} + 14.00 \hat{j}$

(a)The angle betweenA → and B→

$\overset{鈫�}{A} \overset{鈫�}{B} = (- 2 脳 2) + (6 脳 (- 3)) = - 22 A = \sqrt{2^{2} + 6^{2}} = \sqrt{40} = 6.32 B = \sqrt{2^{2} + 3^{2}} = \sqrt{13} = 3.6$

$\cos 胃 = \frac{\overset{鈫�}{A} 路 \overset{鈫�}{B}}{A B} = \frac{60}{\sqrt{34} \sqrt{136}} 胃 = \cos^{- 1} (\frac{60}{\sqrt{34} \sqrt{136}})$

(b) The angle between A→ and B→

$\overset{鈫�}{A} \overset{鈫�}{B} = (- 4 脳 7) + (2 脳 14) = 0 A = \sqrt{4^{2} + 2^{2}} = \sqrt{20} B = \sqrt{7^{2} + 14^{2}} = \sqrt{245} \cos 胃 = \frac{\overset{鈫�}{A} 路 \overset{鈫�}{B}}{A B} = \frac{- 22}{\sqrt{40} \sqrt{13}} 胃 = \cos^{- 1} (\frac{- 22}{\sqrt{40} \sqrt{13}})$

(c) The angle between A→ and B→

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Short Answer

Step by step solution

Given data

(a)The angle betweenA → and B→

(b) The angle between A→ and B→

(c) The angle between A→ and B→

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Find the angle between each of thesepairs of vectors:(a)A鈫�=-2.00i^+6.00j^andB鈫�=2.00i^-3.00j^(b)A鈫�=3.00i^+5.00j^andB鈫�=10.00i^+6.00j^(c) A鈫�=-4.00i^+2.00j^andB鈫�=7.00i^+14.00j^

Short Answer

Step by step solution

Given data

(a)The angle betweenA → and B→

(b) The angle between A→ and B→

(c) The angle between A→ and B→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Particle Model of Matter

Medical Physics

Circular Motion and Gravitation

Quantum Physics

Electricity

Study anywhere. Anytime. Across all devices.