Unit vectors please check my answer

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  • #1
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Homework Statement


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


Homework Equations





The Attempt at a Solution


here is my answer,, please confirm if i'm correct.

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


[itex]\hat{e_{1}}[/itex] = [itex]\frac{5\hat{i} - 3\hat{j} + 2\hat{k}}{\sqrt{38}}[/itex]

am i correct? Please check
 
Last edited:

Answers and Replies

  • #2
SammyS
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Homework Statement


if [itex]\vec{e_{1}}[/itex] = 5[itex]\hat{i}[/itex] - 3[itex]\hat{j}[/itex] + 2[itex]\hat{k}[/itex]

Homework Equations



The Attempt at a Solution

That's not a unit vector.

Please state the problem you're trying to solve.
 
  • #3
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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:
  • #4
SammyS
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The Attempt at a Solution


here is my answer,, please confirm if i'm correct.

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


[itex]\hat{e_{1}}[/itex] = [itex]\frac{5\hat{i} - 3\hat{j} + 2\hat{k}}{\sqrt{38}}[/itex]

am i correct? Please check
Yes. That is correct .
 
  • #5
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Thanks.. Can you please check my other question.. I really appreciate it! Thanks again.
 

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