Chapter 1: Q19P (page 39)

What is the unit vector in the direction of $<2, 2, 2>$ ?What is the unit vector in the direction of $<3, 3, 3>$ ?

Short Answer

Expert verified

The unit vector in the direction of $<2, 2, 2> i s <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}> .$

The unit vector in the direction of $<3, 3, 3> i s <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}> .$

Step by step solution

Definition of unit vector

The unit vector in the direction of a vector is the vector divided by its magnitude that is given by:

$\hat{r} = \frac{\overset{⇀}{r}}{|\overset{⇀}{r}|}$

Calculating unit vector for 2,2,2

Take the square root of sum of square of each component of the vector $<2, 2, 2>$ to obtain its magnitude.

$\sqrt{2^{2} + 2^{2} + 2^{2}} = 2 \sqrt{3}$

Divide the vector by its magnitude to compute its unit vector,

$\hat{r} = \frac{<2, 2, 2>}{2 \sqrt{3}} = <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}>$

Therefore, the unit vector in the direction of $<2, 2, 2> i s <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}> .$

Calculating unit vector for 3,3,3

Take the square root of sum of square of each component of the vector $<3, 3, 3>$ to obtain its magnitude.

$\sqrt{3^{2} + 3^{2} + 3^{2}} = 3 \sqrt{3}$

Divide the vector by its magnitude to compute its unit vector.

$\hat{r} = \frac{<3, 3, 3>}{3 \sqrt{3}} = <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}> T h e r e f o r e, t h e u n i t v e c t o r i n t h e d i r e c t i o n o f <3, 3, 3> i s <\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}>$

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.

What is the unit vector in the direction of $<2, 2, 2>$ ?What is the unit vector in the direction of $<3, 3, 3>$ ?

Short Answer

Step by step solution

Definition of unit vector

Calculating unit vector for 2,2,2

Calculating unit vector for 3,3,3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Measurements

Radiation

Astrophysics

Oscillations

Waves Physics

Study anywhere. Anytime. Across all devices.

What is the unit vector in the direction of 2,2,2?What is the unit vector in the direction of3,3,3?

Short Answer

Step by step solution

Definition of unit vector

Calculating unit vector for 2,2,2

Calculating unit vector for 3,3,3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Measurements

Radiation

Astrophysics

Oscillations

Waves Physics

Study anywhere. Anytime. Across all devices.

What is the unit vector in the direction of $<2, 2, 2>$ ?What is the unit vector in the direction of $<3, 3, 3>$ ?