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math: add colinear points and vevctor details

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eggy 2021-04-25 12:30:28 -04:00
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@ -323,7 +323,12 @@ The special **zero vector** $\vec{0}$ is a vector of undefined direction and zer
Vectors with the same magnitude but opposite directions are equal to one another except one is the negative of the other. Vectors with the same magnitude but opposite directions are equal to one another except one is the negative of the other.
**Colinear** vectors are those that parallel with one another — that is, with identical or opposite directions. **Colinear** vectors are those that parallel with one another — that is, with identical or opposite directions. Vectors that are colinear must also be **scalar multiples** of each other:
$$\vec{u}=k\vec{v}$$
**Position** vectors are vectors where the initial point is at the origin — where the terminal point is $A$, a position vector can be written as $\vec{OA}$.
**Colinear points** are points that lie on the same straight line. If two colinear vectors that share a common point can be formed between three points, those points are colinear.
### Unit vector ### Unit vector
@ -369,6 +374,10 @@ In general, the x-plane is the one in and out of the page, the y-plane left and
Please see [SL Physics 1#Adding/subtracting vectors diagrammatically](/sph3u7/#addingsubtracting-vectors-diagrammatically) for more details. Please see [SL Physics 1#Adding/subtracting vectors diagrammatically](/sph3u7/#addingsubtracting-vectors-diagrammatically) for more details.
The sum of two vectors can also be solved diagrammatically by envisioning the head-to-tail as a parallelogram.
<img src="/resources/images/vector-parallelogram.png" width=700>(Source: Kognity)</img>
## Resources ## Resources
- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf) - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)