- #1
PFStudent
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Homework Statement
Hey,
I had a question about resolving the z-component of a vector.
Lets say that there is a problem that asks us to find the resultant force vector in three-dimensions.
I know that the the resultant force vector, [itex]\vec{F}_{R}[/itex] is given by the sum of its vector components as follows,
[tex]
\vec{F}_R = \vec{F}_{x}\hat{i} + \vec{F}_{y}\hat{j} + \vec{F}_{z}\hat{k}
[/tex]
I know how to find [itex]{F}_{x}[/itex] and [itex]{F}_{y}[/itex],
[tex]
{F}_{x} = \left|\vec{F}\right|{cos}{\theta}
[/tex]
[tex]
{F}_{x} = \left|\vec{F}\right|{sin}{\theta}
[/tex]
but how do I find [itex]{F}_{z}[/itex]?
[tex]
{F}_{z} = ?
[/tex]
I tried looking for this result for a while over the internet with no luck.
Is there a general way. in the same sense that the [itex]x[/itex] and [itex]y[/itex] components use [itex]cos\theta[/itex] and [itex]sin\theta[/itex], to always evaluate the [itex]z[/itex] component in terms of [itex]\theta[/itex]?
Thanks,
-PFStudent
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