Explain the resolution of vectors.

(N/A) In figure $(a)$,$\vec{A}$ and $\vec{B}$ are coplanar and non-parallel vectors.
We want to resolve vector $\vec{R}$ into components along $\vec{A}$ and $\vec{B}$.
Suppose $\vec{OQ}$ represents $\vec{R}$.
In figure $(b)$,draw a line through $O$ parallel to $\vec{A}$ and another line through $Q$ parallel to $\vec{B}$. These two lines intersect at point $P$.
According to the triangle law of vector addition:
$\vec{OQ} = \vec{OP} + \vec{PQ}$
Since $\vec{OP} \parallel \vec{A}$,we can write $\vec{OP} = \lambda \vec{A}$.
Since $\vec{PQ} \parallel \vec{B}$,we can write $\vec{PQ} = \mu \vec{B}$.
(Here,$\lambda$ and $\mu$ are scalar constants).
Therefore,$\vec{R} = \lambda \vec{A} + \mu \vec{B}$.
This means $\vec{R}$ is expressed as the sum of its components in the directions of $\vec{A}$ and $\vec{B}$.