Chapter 3: Q57P (page 60)

If $\vec{B}$ is added to $\vec{A}$ , the result is $6.0 \hat{i} + 1.0 \hat{j}$ . If $\vec{B}$ is subtracted fromrole="math" localid="1656310989938" $\vec{A}$ , the result is $- 4.0 \hat{i} + 7.0 \hat{j}$ . What is the magnitude of role="math" localid="1656311031101" $\vec{A}$ ?

Short Answer

Expert verified

The magnitude of $\vec{A}$ is 4.1

Step by step solution

To understand the concept

This problem deals with the addition and subtraction of vectors.

To find the magnitude of A→

Given,

$\vec{A} + \vec{B} = 6.0 \hat{i} + 1.0 \hat{j} (i) \vec{A} - \vec{B} = - 4.0 \hat{i} + 7.0 \hat{j} (ii)$

Adding equations (i) and (ii),

$(\vec{A} + \vec{B}) + (\vec{A} - \vec{B}) = (6.0 \hat{i} + 1.0 \hat{j}) + (- 4.0 \hat{i} + 7.0 j) 2 \vec{A} ⃗ = (2.0 \hat{i} + 8.0 \hat{j})$

Thus

$\vec{A} = (1.0 \hat{i} + 4.0 \hat{j})$ (iii)

Using equation (iii), the magnitude of $\vec{A}$ is then given by

$A = | A ⃗ | = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}} A = \sqrt{(1.0)^{2} + (4.0)^{2}} A = 4.1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If $\vec{B}$ is added to $\vec{A}$ , the result is $6.0 \hat{i} + 1.0 \hat{j}$ . If $\vec{B}$ is subtracted fromrole="math" localid="1656310989938" $\vec{A}$ , the result is $- 4.0 \hat{i} + 7.0 \hat{j}$ . What is the magnitude of role="math" localid="1656311031101" $\vec{A}$ ?

Short Answer

Step by step solution

To understand the concept

To find the magnitude of A→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Further Mechanics and Thermal Physics

Nuclear Physics

Engineering Physics

Quantum Physics

Electricity

Study anywhere. Anytime. Across all devices.

If B→is added to A→, the result is6.0i^+1.0j^ . If B→is subtracted fromrole="math" localid="1656310989938" A→ , the result is -4.0i^+7.0j^. What is the magnitude of role="math" localid="1656311031101" A→?

Short Answer

Step by step solution

To understand the concept

To find the magnitude of A→

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Further Mechanics and Thermal Physics

Nuclear Physics

Engineering Physics

Quantum Physics

Electricity

Study anywhere. Anytime. Across all devices.

If $\vec{B}$ is added to $\vec{A}$ , the result is $6.0 \hat{i} + 1.0 \hat{j}$ . If $\vec{B}$ is subtracted fromrole="math" localid="1656310989938" $\vec{A}$ , the result is $- 4.0 \hat{i} + 7.0 \hat{j}$ . What is the magnitude of role="math" localid="1656311031101" $\vec{A}$ ?