Q23P A proton is located at <3脳10... [FREE SOLUTION]

Chapter 1: Q23P (page 40)

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

Short Answer

Expert verified

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

(b) The magnitude of $\overset{鈫�}{r}$ is $| \overset{鈫�}{r} | = 9.6 脳 10^{- 10} m$ .

Step by step solution

Given data

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

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

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

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

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

The unit vector along a vector $\overset{鈫�}{r}$ is

$\hat{r} = \frac{\overset{鈫�}{r}}{| \overset{鈫�}{r} |} . . . . . . (III)$

Determining the position vector of the proton

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

$\overset{鈫�}{r} = (3 脳 10^{- 10} \hat{i} - 3 脳 10^{- 10} \hat{j} + 8 脳 10^{- 10} \hat{k}) m$

Determining the magnitude of the position vector of the proton

From equation (II), the magnitude of $\overset{鈫�}{r}$ is

$|\overset{鈫�}{r}| = \sqrt{{(3 脳 10^{- 10})}^{2} + {(- 3 脳 10^{- 10})}^{2} + {(8 脳 10^{- 10})}^{2}} m = \sqrt{3^{2} + 3^{2} + 8^{2}} 脳 10^{- 10} m = 9.06 脳 10^{- 10} m$

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

Determining the unit vector along the position vector of the proton

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

$\overset{鈫�}{r} = \frac{(3 脳 10^{- 10} \hat{i} - 3 脳 10^{- 10} \hat{j} + 8 脳 10^{- 10} \hat{k}) m}{9.06 脳 10^{- 10} m} = 0.33 \hat{i} - 0.33 \hat{j} + 0.883 \hat{k}$

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

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91影视

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

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

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91影视

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

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

Quantum Physics

Space Physics

Fields in Physics

Atoms and Radioactivity

Oscillations

Thermodynamics

Study anywhere. Anytime. Across all devices.

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