Chapter 1: Q23P (page 40)

A proton is located at $< 3 \times 10^{- 10}, - 3 \times 10^{- 10}, 8 \times 10^{- 10} > m$ .
(a)What is $\vec{r}$ , the vector from the origin to the location of the proton?
(b)What is $| \vec{r} |$ ?
(c)What is $\hat{r}$ , the unit vector in the direction of $\vec{r}$ ?

Short Answer

Expert verified

(a) The vector from the origin to the location of the proton is $\vec{r} = (3 \times 10^{- 10} \hat{i} - 3 \times 10^{- 10} \hat{j} + 8 \times 10^{- 10} \hat{k}) m$ .

(b) The magnitude of $\vec{r}$ is $| \vec{r} | = 9.6 \times 10^{- 10} m$ .

Step by step solution

Given data

Location of the proton is $r = < 3 \times 10^{- 10}, - 3 \times 10^{- 10}, 8 \times 10^{- 10} > m$

Position vector, magnitude of a vector and unit vector

The position vector of a location $<x, y, z>$ with respect to origin $<0, 0, 0>$ is

$\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} . . . . . . (l)$

The magnitude of a vector $\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}$ is

$| \vec{r} | = \sqrt{x^{2} + y^{2} + z^{2}} . . . . . (ll)$

The unit vector along a vector $\vec{r}$ is

$\hat{r} = \frac{\vec{r}}{| \vec{r} |} . . . . . . (III)$

Determining the position vector of the proton

From equation (I), the position vector of the proton is

$\vec{r} = (3 \times 10^{- 10} \hat{i} - 3 \times 10^{- 10} \hat{j} + 8 \times 10^{- 10} \hat{k}) m$

Determining the magnitude of the position vector of the proton

From equation (II), the magnitude of $\vec{r}$ is

$|\vec{r}| = \sqrt{{(3 \times 10^{- 10})}^{2} + {(- 3 \times 10^{- 10})}^{2} + {(8 \times 10^{- 10})}^{2}} m = \sqrt{3^{2} + 3^{2} + 8^{2}} \times 10^{- 10} m = 9.06 \times 10^{- 10} m$

Thus, the required magnitude is $9.06 \times 10^{- 10} m$

Determining the unit vector along the position vector of the proton

From equation (III), the unit vector along $\vec{r}$ is

$\vec{r} = \frac{(3 \times 10^{- 10} \hat{i} - 3 \times 10^{- 10} \hat{j} + 8 \times 10^{- 10} \hat{k}) m}{9.06 \times 10^{- 10} m} = 0.33 \hat{i} - 0.33 \hat{j} + 0.883 \hat{k}$

Thus, the required unit vector is $0.33 \hat{i} - 0.33 \hat{j} + 0.883 \hat{k}$

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A proton is located at $< 3 \times 10^{- 10}, - 3 \times 10^{- 10}, 8 \times 10^{- 10} > m$ .
(a)What is $\vec{r}$ , the vector from the origin to the location of the proton?
(b)What is $| \vec{r} |$ ?
(c)What is $\hat{r}$ , the unit vector in the direction of $\vec{r}$ ?

Short Answer

Step by step solution

Given data

Position vector, magnitude of a vector and unit vector

Determining the position vector of the proton

Determining the magnitude of the position vector of the proton

Determining the unit vector along the position vector of the proton

One App. One Place for Learning.

Most popular questions from this chapter

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A proton is located at <3×10-10,-3×10-10,8×10-10>m.(a)What is r→, the vector from the origin to the location of the proton?(b)What is |r→|?(c)What is r^, the unit vector in the direction of r→?

Short Answer

Step by step solution

Given data

Position vector, magnitude of a vector and unit vector

Determining the position vector of the proton

Determining the magnitude of the position vector of the proton

Determining the unit vector along the position vector of the proton

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Magnetism

Space Physics

Measurements

Atoms and Radioactivity

Electrostatics

Study anywhere. Anytime. Across all devices.

A proton is located at $< 3 \times 10^{- 10}, - 3 \times 10^{- 10}, 8 \times 10^{- 10} > m$ .
(a)What is $\vec{r}$ , the vector from the origin to the location of the proton?
(b)What is $| \vec{r} |$ ?
(c)What is $\hat{r}$ , the unit vector in the direction of $\vec{r}$ ?