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 $\frac{2}{3} i - \frac{2}{3} j + \frac{1}{3} k$ .

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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.

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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

Magnetism

Further Mechanics and Thermal Physics

Oscillations

Quantum Physics

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Electricity and Magnetism

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 $\hat{r}$