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

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

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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→

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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

Oscillations

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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" $\vec{A}$ ?