alvierahman90/notes
1
1
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

fix vector formatting issue

Browse Source
This commit is contained in:
Akbar Rahman 2022-03-02 01:34:03 +00:00
parent f6ce1dedd6
commit a8de6477af
Signed by: alvierahman90
GPG Key ID: 20609519444A1269
1 changed files with 3 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

5
uni/mmme/1026_maths_for_engineering/vectors.md
View File

@ -248,7 +248,7 @@ $$\frac{x-x_0}{d_1} = \frac{y-y_0}{d_2} = \frac{z-z_0}{d_3}$$
A *plane* can be defined by specifying either: A *plane* can be defined by specifying either:
- three points (as long as they're not in a straight line) - three points (as long as they're not in a straight line)
- a point on the plne and two directions (useful for a parametric form) - a point on the plane and two directions (useful for a parametric form)
- specifying a point on the plane and the normal vector to the plane - specifying a point on the plane and the normal vector to the plane
#### Specifying a Point and a Normal Vector #### Specifying a Point and a Normal Vector
@ -263,7 +263,7 @@ $$(\pmb r - \pmb a) \cdot \pmb n = 0$$
So the *vector equation* of the plane is So the *vector equation* of the plane is
$$\pmb r \cdot \pmb n = \pmb a \cdot n = d$$ $$\pmb r \cdot \pmb n = \pmb a \cdot \pmb n = \pmb d$$
where $\pmb r = (x, y, z)$ and the vectors $\pmb a$ and $\pmb n$ are known. where $\pmb r = (x, y, z)$ and the vectors $\pmb a$ and $\pmb n$ are known.
@ -291,6 +291,7 @@ and so the equation of the plane is
$$(\pmb r - \pmb a)\cdot((\pmb c - \pmb a)\times(\pmb c - \pmb b)) = 0$$ $$(\pmb r - \pmb a)\cdot((\pmb c - \pmb a)\times(\pmb c - \pmb b)) = 0$$
#### The Angle Between Two Planes #### The Angle Between Two Planes
... is the same as the angle between their normal vectors ... is the same as the angle between their normal vectors