When making component vectors, can either do it from the vertical or horizontal, but remember to check for signs!!!
If you arrange the side lengths in your head it should yield negatives, but if not just look at the vector (e.g. if it goes top to bottom right then obviously the vertical component is negative)
Given a vector $v$, the unit vector in the direction of $v$ has magnitude 1. In general, the unit means it has a magnitude of 1.
Say we have vector $v$ with magnitude of $5$.
The unit vector of $v$ points in the same direction of $v$ but has a magnitude of 1.
To change a vector's magnitude without changing its direction, we must multiply (or divide but divide sus) by a positive number.
Hence the unit vector of $v$ is $\frac{1}{5}v$.
For vector $v$ of magnitude $|v|$,
$\vec{\hat{v}}=\frac{1}{|v|}v$
Why do we use unit vectors?
If we have a bunch of vectors in the same direction, we can represent them as their magnitude times the unit vector
e.g. Vector A = $5\vec{\hat{v}}$ Vector B = $10\vec{\hat{v}}$ Vector C = $1239121347120348213\vec{\hat{v}}$
Vector questions can involve setting up equations and solving them.
Remember that two vectors are equal if and only if their magnitudes and directions are equal.
Equivalently, two vectors in component form are equal if and only if their components are equal.
i.e.
$ai+bj=ci+dj$ if and only if $a=c,b=d$
Solving equations with vectors in component form usually involves equating components.
We must write out the zero vector in full for working out marks!!
i.e. $0i+0j$
When drawing vector diagrams, don't mix up displacement and velocity vectors, cause that is sussy and doesn't make much sense. Make the velocity smaller than the direction (i.e. dont make one big triangle)
