Q. 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 is :

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A

$\sqrt{3} N$

B

$\frac{\sqrt{3}}{2} N$

C

$\frac{3}{2} N$

D

Zero

Solution:

$ \vec{F} =1 \hat{i}-1 \hat{j}-\frac{3}{2} \hat{i}+\sqrt{3} \hat{j}-\frac{3 \sqrt{3}}{2} \hat{j} $
$ \vec{F} =\frac{-3}{2} \hat{i}-\frac{\sqrt{3}}{2} \hat{j} $
$|\vec{F}| =\sqrt{\frac{9}{4}+\frac{3}{4}}=\sqrt{\frac{12}{4}}=\sqrt{3} N$

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