Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that |AB| = |BC| = |CD|, then AB + AC + AD = 4AO + OB + OC
Reason R: Polygon law of vector addition yields AB + BC + CD = AD = 2AO

In the light of the above statements, choose the most appropriate answer from the options given below:

From triangle law of addition, we can clearly write answer.

$\left|\overrightarrow{P}\right|=\left|\overrightarrow{Q}\right|=x$

let the angle between $\overrightarrow{P}and\overrightarrow{Q}$ $\stackrel{}{}\stackrel{}{}$ is , so according to question, we can write $\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\text{exception 25:}\text{exception 25:}$

^{$\left|\overrightarrow{P}+\overrightarrow{Q}\right|=n\times \left|\overrightarrow{P}-\overrightarrow{Q}\right|\Rightarrow \sqrt[]{P^2+Q^2+2PQcos\theta }=n\times \sqrt[]{P^2+Q^2-2PQcos\theta }$}

$\Rightarrow \sqrt[]{x^2+x^2+2x^{2}cos\theta }=n\times \sqrt[]{x^2+x^2-2x^{2}cos\theta }$

$\Rightarrow \theta =co{s}^{-1}\left(\frac{n^2-1}{n^2+1}\right)$

Graphically, we place vectors head-to-tail. Analytically, we add components along axes using coordinate geometry, trigonometric functions, and unit vectors for precise vector resultant calculation.

It resolves vectors into components, adds corresponding x and y values algebraically, then reconstructs the resultant using magnitude and direction. That is, applying vector addition rules.