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Unit Vectors and Vector Components

by Alexrey
Tags: components, unit, vector, vectors
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Alexrey
#1
Oct30-13, 05:59 PM
P: 34
I remember in my first year physics classes, when dealing with a force F we would find the vector's x- and y-components using [tex]F_x=r cos(θ)[/tex] and [tex]F_y=r sin(θ)[/tex] I also remember learning in my mathematics classes about unit vectors, but cannot seem to remember using them to break vectors down into their respective x- and y-components. As such, I thought I'd ask this question: Am I correct in thinking that when using a Cartesian coordinate system to describe a force F, if we find the unit vector for F, are the x- and y- components of this unit vector equivalent to [tex]cos(θ)[/tex] and [tex]sin(θ)[/tex] respectively?
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Mark44
#2
Oct30-13, 07:18 PM
Mentor
P: 21,402
Quote Quote by Alexrey View Post
I remember in my first year physics classes, when dealing with a force F we would find the vector's x- and y-components using [tex]F_x=r cos(θ)[/tex] and [tex]F_y=r sin(θ)[/tex] I also remember learning in my mathematics classes about unit vectors, but cannot seem to remember using them to break vectors down into their respective x- and y-components. As such, I thought I'd ask this question: Am I correct in thinking that when using a Cartesian coordinate system to describe a force F, if we find the unit vector for F, are the x- and y- components of this unit vector equivalent to [tex]cos(θ)[/tex] and [tex]sin(θ)[/tex] respectively?
Yes, assuming θ is the angle that F makes with the x-axis.

Think about it.
Fx = |F| cos(θ)
Fy = |F| sin(θ)

To get unit vectors, divide each of the above by its magnitude, |F|.
Alexrey
#3
Nov1-13, 05:28 PM
P: 34
Great, thank you.


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