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education/math/MATH1060 (trig)/Vectors.md
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@ -47,5 +47,11 @@ If $\theta (0\degree < \theta < 180\degree)$, is the angle between two nonzero v
$$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$ $$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$
# Work # Work
The dot product can be used to compute the work required to move an object a certain distance.
To compute work, you need a force and direction. If the force is applied in the same direction:
$$ W = Fd $$
The work $W$ is done by a constant force $\vec{F}$ in moving an object from a point $P$ to a point $Q$ is defined by: The work $W$ is done by a constant force $\vec{F}$ in moving an object from a point $P$ to a point $Q$ is defined by:
$$ W = \vec{p} \cdot\vec{PQ} = |\vec{F}||\vec{PQ}|\cos\theta $$ $$ W = \vec{F} \cdot\vec{PQ} = |\vec{F}||\vec{PQ}|\cos\theta $$Where $\theta$ is the angle between $\vec{F}$ and $\vec{PQ}$.