Chapter 1: Q7P (page 9)

Find the separation vector r from the source point (2,8,7) to the field point ( 4,6,8). Determine its magnitude ( r ), and construct the unit vector $\hat{r}$

Short Answer

Expert verified

The magnitude is 3 and unit separation vector is $\frac{2}{3} i - \frac{2}{3} j + \frac{1}{3} k$ .

Step by step solution

Explain the concept and write the expression of position vector

The separation vector is obtained by subtracting the source vector ${\vec{r}}_{2}$ from the destination vector ${\vec{r}}_{1}$ . The expression of position vector is as follows:

$\vec{r} = x i + y j + z k$

Where $i, j, k$ are unit vectors along $x, y, z$ coordintaes

Find the separation vector

The position vector at $(2, 8, 7)$ is $\vec{r} = 2 i + 8 j + 7 k$ , and position vector at $(4, 6, 8)$ isrole="math" localid="1657351115792" $\vec{r} = 4 i + 6 j + 8 k$

The separation vector is given as $\vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1}$ .

Substitute $2 i + 8 j + 7 k$ for ${\vec{r}}_{1}$ , and $4 i + 6 j + 8 k$ for ${\vec{r}}_{2}$ into $\vec{r} = {\vec{r}}_{2} - {\vec{r}}_{1}$

$\vec{r} = 4 i + 6 j + 8 k - 2 i - 8 j - 7 k \vec{r} = 2 i - 2 j + k$

find the magnitude of separation vector

Find the magnitude of separation vector.

$|\vec{r}| = \sqrt{{(2)}^{2} + {(- 2)}^{2} + {(1)}^{2}} |\vec{r}| = 3$

Find the unit separation vector

Divide the separation vector by its magnitude to find unit separation vector.

$\hat{r} = \frac{\vec{r}}{|\vec{r}|} = \frac{2 i - 2 j + k}{3} = \frac{2}{3} i - \frac{2}{3} j + \frac{1}{3} k$

Thus the unit separation vector is $\frac{2}{3} i - \frac{2}{3} j + \frac{1}{3} k$ .

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.

Find the separation vector r from the source point (2,8,7) to the field point ( 4,6,8). Determine its magnitude ( r ), and construct the unit vector $\hat{r}$

Short Answer

Step by step solution

Explain the concept and write the expression of position vector

Find the separation vector

find the magnitude of separation vector

Find the unit separation vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Classical Mechanics

Mechanics and Materials

Electricity and Magnetism

Wave Optics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

Find the separation vector r from the source point (2,8,7) to the field point ( 4,6,8). Determine its magnitude ( r ), and construct the unit vector r^

Short Answer

Step by step solution

Explain the concept and write the expression of position vector

Find the separation vector

find the magnitude of separation vector

Find the unit separation vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Classical Mechanics

Mechanics and Materials

Electricity and Magnetism

Wave Optics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

Find the separation vector r from the source point (2,8,7) to the field point ( 4,6,8). Determine its magnitude ( r ), and construct the unit vector $\hat{r}$