Question

Can anyone do this? This question is from Vectors and Forces

Answer 1

Please refer to the image below

Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

$\huge{\gray{\mathrm{Given:-}}}$

$\large{\sf{\vec{a} \: = \: 3 \:}}$

$\large{\sf{ \vec{b} \: = \: 2 }}$

$\large{\sf{\theta \: = \: 120^{\circ}}}$

_______________________________

$\huge{\gray{\mathrm{To \: find :-}}}$

Resultant force

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$\huge{\gray{\mathrm{Solution :-}}}$

We have formula,

$\LARGE \star {\underline{\boxed{\sf{R \: = \: \sqrt{a^2 \: + \: b^2 \: + \: 2ab cos \theta}}}}}$

_________________[Put Values]

$\Large \leadsto {\sf{R \: = \: \sqrt{(3)^2 \: + \: (2)^2 \: + \: 2(3)(2) Cos120^{\circ}}}}$

$\Large \leadsto {\sf{R \: = \: \sqrt{9 \: + \: 4 \: + \cancel{12} \: \times \: \cancel{\frac{-1}{2}}}}}$

$\Large \leadsto {\sf{R \: = \: \sqrt{13 \: - \: 6}}}$

$\Large \leadsto {\sf{R \: = \: \sqrt{9}}}$

$\Huge \implies {\boxed{\boxed{\sf{R \: = \: 3}}}}$

∴ Force is 3 N