Explain the parallelogram method for vector addition. Also,explain how this is comparable to the triangle method.

(N/A) $1$. Consider two vectors $\vec{A}$ and $\vec{B}$ as shown in figure $(a)$.
$2$. To add them using the parallelogram method,place the tails of both vectors at a common point $O$ as shown in figure $(b)$.
$3$. Construct a parallelogram $OPSQ$ such that $\vec{A}$ and $\vec{B}$ are adjacent sides. The diagonal $OS$ starting from $O$ represents the resultant vector $\vec{R} = \vec{A} + \vec{B}$.
$4$. In the triangle method,we place the tail of $\vec{B}$ at the head of $\vec{A}$. The resultant is the vector from the tail of $\vec{A}$ to the head of $\vec{B}$,as shown in figure $(c)$.
$5$. Since the side $PS$ in the parallelogram is parallel and equal to $OQ$ (which is $\vec{B}$),the triangle $OPS$ in the parallelogram method is identical to the triangle formed in the triangle method.
$6$. Thus,both methods yield the same resultant vector $\vec{R}$.
$7$. The magnitude of the resultant vector satisfies the triangle inequality: $|\vec{R}| \leq |\vec{A}| + |\vec{B}|$.