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.

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

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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

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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

Magnetism and Electromagnetic Induction

Particle Model of Matter

Medical Physics

Circular Motion and Gravitation

Quantum Physics

Dynamics

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 $<3, 3, 3>$ ?