State and explain tringal law of vector addiction

The triangle law of vector addition states that:

If two vectors are represented in magnitude and direction by the two sides of a triangle taken in the same order, then their resultant (sum) is represented in magnitude and direction by the third side of the triangle taken in the opposite order.

Explanation:
Consider two vectors, $\vec{A}$ and $\vec{B}$.

1. Draw vector $\vec{A}$ from an initial point P to a terminal point Q.
2. From the terminal point Q of vector $\vec{A}$, draw vector $\vec{B}$ to a terminal point R.
3. The resultant vector, $\vec{R}$, is obtained by drawing a vector from the initial point P of $\vec{A}$ to the terminal point R of $\vec{B}$.

Mathematically, this is expressed as:

$$\vec{R} = \vec{A} + \vec{B}$$

This law is fundamental for finding the sum of two vectors graphically.