arc/notes
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2024-12-02 10:18:13

Browse Source
This commit is contained in:
arc 2024-12-02 10:18:13 -07:00
parent 0356193ef6
commit c01734fb7a
1 changed files with 6 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

7
education/math/MATH1060 (trig)/Vectors.md
View File

@ -39,4 +39,9 @@ $$ \vec{v} = \langle \cos \theta,\ |\vec{v}|\sin\theta \rangle $$
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 $\vec{u} * \vec{v}$.
- $\vec{u} * \vec{v} = -7 * -4 + 3 * 4$
- $\vec{u} * \vec{v} = -7 * -4 + 3 * 4$
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
$$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$