diff --git a/docs/mcv4u7.md b/docs/mcv4u7.md index cc8b19c..9b914bf 100644 --- a/docs/mcv4u7.md +++ b/docs/mcv4u7.md @@ -464,6 +464,23 @@ In three dimensions, there is a final possibility should the lines not be parall For an object moving at **constant velocity in 2D space**, where $\vec{s}$ is its displacement, $\vec{s}_0$ is its initial displacement at $t=0$, $t$ is the time elapsed, and $\vec{v}$ is its velocity: $$\vec{s}=\vec{s}_0+t\vec{v}$$ +### Vector projections + +If two vectors $\vec{a}$ and $\vec{b}$ are placed tail-to-tail, the **component** of $\vec{a}$ in the direction of $\vec{b}$ is known as the **vector projection of $\vec{a}$ onto $\vec{b}$**. Represented by $Projection$, its magnitude is called the **scalar projection**. +$$Proj_\vec{b}\vec{a}=\biggr(\frac{\vec{a}\bullet\vec{b}}{|\vec{b}|^2}\biggr)\vec{b}$$ + +$$ +\begin{align*} +|Proj_\vec{b}\vec{a}|&=\frac{\vec{a}\bullet\vec{b}}{|\vec{b}|} \\ +&=|\vec{a}|\cos\theta +\end{align*} +$$ + +!!! warning + The magnitude of any projection is always **positive**. If $\cos\theta$ returns a negative value, it needs to be absed again. + +Vector projections are applied in work equations — see [SL Physics 1](/sph3u7/#work) for more information. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)