diff --git a/education/math/MATH1060 (trig)/Vectors.md b/education/math/MATH1060 (trig)/Vectors.md index 1ed8a8b..2f10e88 100644 --- a/education/math/MATH1060 (trig)/Vectors.md +++ b/education/math/MATH1060 (trig)/Vectors.md @@ -38,13 +38,13 @@ $$ \vec{v} = \langle \cos \theta,\ |\vec{v}|\sin\theta \rangle $$ # The Dot Product The dot product of two vectors $\vec{u} = \langle a, b \rangle$ and $\vec{v} = \langle c, d \rangle$ is $\vec{u} * \vec{v} = ac + bd$. -- Given that $\vec{u} = \langle -7, 3 \rangle$, and $\vec{v} = \langle -3, 4 \rangle$, find $\vec{u} * \vec{v}$. -- $\vec{u} * \vec{v} = -7 * -4 + 3 * 4$ +- Given that $\vec{u} = \langle -7, 3 \rangle$, and $\vec{v} = \langle -3, 4 \rangle$, find $\vec{u} \cdot \vec{v}$. +- $\vec{u} \cdot \vec{v} = -7 \cdot -4 + 3 \cdot 4$ The dot product can be used to find the angle between two vectors. If $\theta (0\degree < \theta < 180\degree)$, is the angle between two nonzero vectors $\vec{u}$ and $\vec{v}$, then -$$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$ +$$ \cos\theta = \dfrac{\vec{u}\cdot\vec{v}}{|\vec{u}||\vec{v}|} $$ # Work The dot product can be used to compute the work required to move an object a certain distance.