My Math Forum The Perpendicular Unit Vectors i and j

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February 8th, 2012, 12:39 PM   #1
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The Perpendicular Unit Vectors i and j

Hello. For this question, I have included a diagram to better illustrate my approach. I think the book may be incorrect, as the point m would be some way off from where it would need to be in order to form a parallelogram. Can anyone help me confirm if I have this right or not?
Many thanks.
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February 8th, 2012, 01:41 PM   #2
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Re: The Perpendicular Unit Vectors i and j

Hello, bilano99!

Sorry, the book is right . . .

Quote:
 $\text{Given: }\:\vec h \:=\:6\vec i\,-\,8\vec j,\;\vec k \:=\:4\vec i\,-\,3\vec j$ $\text{If }ohkm\text{ is a parallelogram, where }o\text{ is the origin,}$ [color=beige]. . [/color]$\text{express }\vec m\text{ in terms of }\vec i\text{ and }\vec j.$

The graph looks like this.
(Use the scroll bar to see the entire diagram.)
Code:
          |
m o   |
* *|
* | *
*|    *
- - - - o - - - * - - - - - - - - - - -
|  *       *
|     *       o k
|        *     *
|           *   *
|              * *
|                 o h
|
$\text{W\!e see that: }\:\vec{om} \,=\, \vec{hk}$

$\vec{hk}\:=\:(4i\,-\,3j)\,-\,(6i\,-\,8j) \:=\:-2i\,+\,5h \:=\:\vec{om}$

$\text{(You found }\vec{kh}\text{, you see.)$

 February 8th, 2012, 01:49 PM #3 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Re: The Perpendicular Unit Vectors i and j Ok, I'll give it a second look. Thank you.

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