How to Find the Unit Vector of a Given Vector?

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Homework Help Overview

The discussion revolves around finding the unit vector of a given vector v = <3, -4>. Participants are exploring the concept of unit vectors and the necessary calculations involved in determining them.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to find the length of a vector and the relationship between a vector and its magnitude. There are attempts to clarify the formula for calculating the magnitude and how it relates to finding the unit vector.

Discussion Status

The discussion has progressed with some participants confirming the calculation of the vector's magnitude and suggesting the resulting unit vector. However, there is no explicit consensus on the final representation of the unit vector.

Contextual Notes

Some participants question the initial steps and the formulas used, indicating potential confusion about the calculations involved in finding the unit vector.

huntingrdr
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Homework Statement


Given vector v = <3, -4>, find a unit vector u in the direction of vector v. Give your answer for u as
u = <a, b>
and
u = ai + bj



Homework Equations



none

The Attempt at a Solution



Would I use y2-y1 and x2-x1?
 
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Do you know how to find the length of a vector? If so, use the fact that any vector divided by its length will have a length of 1 (i.e., it will be a unit vector).
 
A unit vector is given by a vector divided by its magnitude. To find a vector's magnitude, or length, use v=sqrt[x^2+y+2].
 
OK, so I got the magnitude of the vector to be 5. So does that mean the answer would be 3/5 i - 4/5 j and <3/5 , -4/5>
 
That's it!
 
Thanks!
 

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