Chapter 4: Q3P (page 84)

A positron undergoes a displacement $^{∆ \vec{r} = 2.0 \hat{i} - 3.0 \hat{j} + 6.0 \hat{k}}$ , ending with the position vector localid="1654329593013" $^{\vec{r} = 3.0 \hat{j} - 4.0 \hat{k}}$ , in meters. What was the positron’s initial position vector?

Short Answer

Expert verified

The initial position vector of positron is $\vec{r_{0}} = (- 2.0 m) \hat{i} + (6.0 m) \hat{j} + (- 10.0 m) \hat{k} .$

Step by step solution

Given data

The displacement of the positron, $∆ \vec{r} = (2.0 m) \hat{i} - (3.0 m) \hat{j} + (6.0 m) \hat{k}$

The final position vector, $\hat{r} = (3.0 m) \hat{j} - (4.0 m) \hat{k}$

Understanding the position vector and displacement vector

In a coordinate system, the position vector gives the location of an object relative to the origin. The displacement vector gives the change in the position of an object.

The expression for the displacement vector is given as:

$∆ \vec{r} = \vec{r} - ∆ \vec{r_{0}}$ … (i)

Here, $^{\vec{r_{0}}}$ and $^{\vec{r}}$ are the position vectors for initial and final positions respectively.

Determination of the initial position vector of positron

Using equation (i), the initial position vector can be calculated as:

${\vec{r}}_{0} = \vec{r} - ∆ \vec{r} = \{(3.0 m) \hat{j} - (4.0 m) \hat{k}\} - \{(2.0 m) \hat{i} - (3.0 m) \hat{j} + (6.0) \hat{k}\} = (2.0 m) \hat{i} + (6.0) \hat{j} + (- 10.0 m) \hat{k}$

Thus, the initial position vector of positron is $\vec{r_{0}} = (- 2.0 m) \hat{i} + (6.0 m) \hat{j} + (- 10.0 m) \hat{k} .$

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.

A positron undergoes a displacement $^{∆ \vec{r} = 2.0 \hat{i} - 3.0 \hat{j} + 6.0 \hat{k}}$ , ending with the position vector localid="1654329593013" $^{\vec{r} = 3.0 \hat{j} - 4.0 \hat{k}}$ , in meters. What was the positron’s initial position vector?

Short Answer

Step by step solution

Given data

Understanding the position vector and displacement vector

Determination of the initial position vector of positron

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Electric Charge Field and Potential

Electromagnetism

Kinematics Physics

Electricity

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

A positron undergoes a displacement∆r→=2.0i^-3.0j^+6.0k^, ending with the position vector localid="1654329593013" r→=3.0j^-4.0k^, in meters. What was the positron’s initial position vector?

Short Answer

Step by step solution

Given data

Understanding the position vector and displacement vector

Determination of the initial position vector of positron

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Electric Charge Field and Potential

Electromagnetism

Kinematics Physics

Electricity

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

A positron undergoes a displacement $^{∆ \vec{r} = 2.0 \hat{i} - 3.0 \hat{j} + 6.0 \hat{k}}$ , ending with the position vector localid="1654329593013" $^{\vec{r} = 3.0 \hat{j} - 4.0 \hat{k}}$ , in meters. What was the positron’s initial position vector?