Chapter 1: 10DQ (page 27)

Is the vector $(\overset{⏞}{i} + \overset{⏞}{j} + \overset{⏞}{k})$ a unit vector? Is the vector $(3.0 \overset{⏞}{i} - 2.0 \overset{⏞}{j})$ a unit vector? Justify your answers.

Short Answer

Expert verified

The vectors $(\overset{⏞}{i} + \overset{⏞}{j} + \overset{⏞}{k})$ and $(3.0 \overset{⏞}{i} - 2.0 \overset{⏞}{j})$ are not a unit vector.

Step by step solution

Introduction

Unit vectors are the vectors whose magnitude is exactly 1 unit. They are very useful for various reasons. Specifically, the unit vectors $[0, 1]$ and $[1, 0]$ can together form any other vector.

Explanation

Unit Vector – A unit vector is a vector with magnitude 1.

Let the vector $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ .

Magnitude:

$\begin{array}{rcl} |\overset{⇀}{a}| & = & \sqrt{1^{2} + 1^{2} + 1^{2}} \\ = & \sqrt{3} \end{array}$

Since magnitude is not 1, $\overset{⇀}{a}$ is not a unit vector.

Likewise, assume the vector $\vec{b} = 3.0 \hat{i} - 2.0 \hat{j}$ .

The amplitude of the vector is

$\begin{array}{rcl} |\vec{b}| & = & \sqrt{3^{2} + 2^{2}} \\ = & \sqrt{9 + 4} \\ = & \sqrt{13} \end{array}$

Which is not equal to 1.

Hence, it is not a unit vector.

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Is the vector $(\overset{⏞}{i} + \overset{⏞}{j} + \overset{⏞}{k})$ a unit vector? Is the vector $(3.0 \overset{⏞}{i} - 2.0 \overset{⏞}{j})$ a unit vector? Justify your answers.

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Introduction

Explanation

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Is the vector(i⏞+j⏞+k⏞) a unit vector? Is the vector(3.0i⏞-2.0j⏞) a unit vector? Justify your answers.

Short Answer

Step by step solution

Introduction

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Famous Physicists

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Study anywhere. Anytime. Across all devices.

Is the vector $(\overset{⏞}{i} + \overset{⏞}{j} + \overset{⏞}{k})$ a unit vector? Is the vector $(3.0 \overset{⏞}{i} - 2.0 \overset{⏞}{j})$ a unit vector? Justify your answers.