Question

The direction of three forces 1 N, 2 N and 3 N acting at a point are parallel to the sides of an equilateral triangle taken in order. The magnitude of their resultant in newton upto 2 decimal places is

Answer 1

Resultant force at the given point is
$\overrightarrow{F}=1\hat{i}-1\hat{i}-\frac{3}{2}\hat{i}+\sqrt{3}\hat{j}-\frac{3\sqrt{3}}{2}\hat{j}$
$\overrightarrow{F}=\frac{-3}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j}$
$|\overrightarrow{F}|=\sqrt{\frac{9}{4}+\frac{3}{4}}=\sqrt{\frac{12}{4}}=\sqrt{3}N$

Why this question? Concept: This is a classic example that any number of vectors can be easily added after breaking them into components, and vectorially adding their respective components.