What is the correct way to calculate unit vectors for given vector components?

AI Thread Summary
To calculate unit vectors from given vector components, the correct approach involves dividing each component by the vector's magnitude. The components provided are -3.20 for x and 2.10 for y. The calculations yielded unit vector components of approximately -0.836 for x and 0.549 for y, which were initially rejected by the system. However, it was clarified that the calculations were unnecessary, as the unit vector should simply maintain the same direction with a magnitude of 1. Ultimately, the confusion stemmed from misinterpreting the problem's requirements regarding unit vector notation.
H2Owned
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Homework Statement


http://img22.imageshack.us/img22/1254/10031833.jpg


Homework Equations





The Attempt at a Solution


My attempt was based on the idea that both triangles formed by the vector components (x component, y component, and the hypotenuse which is the magnitude of the vector itself) would be similar.

I took the length of each of the sides, -3.20 for x and 2.10 for y and individually solved for the unit vector by setting up this relationship:
(length of component)/(length of hypotenuse)=(length unit component)/1

The system rejected both of my answers. For x i got -0.836 and for y i got 0.549.
 
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H2Owned said:

Homework Statement


http://img22.imageshack.us/img22/1254/10031833.jpg


Homework Equations





The Attempt at a Solution


My attempt was based on the idea that both triangles formed by the vector components (x component, y component, and the hypotenuse which is the magnitude of the vector itself) would be similar.

I took the length of each of the sides, -3.20 for x and 2.10 for y and individually solved for the unit vector by setting up this relationship:
(length of component)/(length of hypotenuse)=(length unit component)/1

The system rejected both of my answers. For x i got -0.836 and for y i got 0.549.

Your answer looks fine to me. I calculated the same value for the two components. I like that similar triangle method to find unit vectors. In vector classes, you usually just think about it this way(which involves the exact same math): you have a vector A with magnitude A at angle C. You want the same direction(the same angle C) at a magnitude of 1, so you divide by A(the hypotenuse). So yeah, it's the same calculation: each component divided by the hypotenuse.
 
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Maybe it has to do something with unit vector notation. is there a specific notation?Or maybe we both got the answer wrong. Either way I am not getting my homework credit right now
 
please help me figure this out, or at least give me your opinions.
 
What are you calculating here? Are not the components given in the problem?
The x component is -3.20 and the y component is +2.10, according to the problem. Am I missing something here?
 
nasu said:
What are you calculating here? Are not the components given in the problem?
The x component is -3.20 and the y component is +2.10, according to the problem. Am I missing something here?

it turns out that there isn't any calculation necessary, and your answer is correct. i thought the question was asking for a unit vector with the same angle as the given vector.
A Unit vector is a vector with a magnitude of 1, that's where all of my calculations came from - which apparently were unnecessary.
 

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