## Homework Statement

if $\vec{e_{1}}$ = 5$\hat{i}$ - 3$\hat{j}$ + 2$\hat{k}$ what is the unit vector $\hat{e_{1}}$

## The Attempt at a Solution

$|$$\hat{e_{1}}$$|$ = $\sqrt{\vec{e_{1}} . \vec{e_{1}}}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(5\hat{i} - 3\hat{j} + 2\hat{k}) . (5\hat{i} - 3\hat{j} + 2\hat{k})}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(5\hat{i}) . (5\hat{i}) + (-3\hat{j}) . (-3\hat{j}) + (2\hat{k}) . (2\hat{k})}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(25+9+4)}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{38}$

$\hat{e_{1}}$ = $\frac{5\hat{i} - 3\hat{j} + 2\hat{k}}{\sqrt{38}}$

Last edited:

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

if $\vec{e_{1}}$ = 5$\hat{i}$ - 3$\hat{j}$ + 2$\hat{k}$

## The Attempt at a Solution

That's not a unit vector.

Please state the problem you're trying to solve.

That's not a unit vector.

Please state the problem you're trying to solve.

sorry i wasn't finished editing yet earlier.. please check my solution now. Thanks

Last edited:
SammyS
Staff Emeritus
Homework Helper
Gold Member

## The Attempt at a Solution

$|$$\hat{e_{1}}$$|$ = $\sqrt{\vec{e_{1}} . \vec{e_{1}}}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(5\hat{i} - 3\hat{j} + 2\hat{k}) . (5\hat{i} - 3\hat{j} + 2\hat{k})}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(5\hat{i}) . (5\hat{i}) + (-3\hat{j}) . (-3\hat{j}) + (2\hat{k}) . (2\hat{k})}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{(25+9+4)}$
$|$$\hat{e_{1}}$$|$ = $\sqrt{38}$

$\hat{e_{1}}$ = $\frac{5\hat{i} - 3\hat{j} + 2\hat{k}}{\sqrt{38}}$