find the resultant force of a system of three forces O^− P^→ =9N,O^− R^→ =10N and O^− Q^→ 10N acting at point O where angle POR is 135°,angle POQ is 135° and QOR is 90°


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Question Number 62585 by Jmasanja last updated on 23/Jun/19

$f i n d t h e r e s u l t a n t f o r c e o f a s y s t e m$ $o f t h r e e f o r c e s \bar{O} \vec{P} = 9 N, \bar{O} \vec{R} = 10 N a n d \bar{O} \vec{Q} 10 N$ $a c t i n g a t p o i n t O w h e r e a n g l e P O R i s$ $135 °, a n g l e P O Q i s 135 ° a n d Q O R i s$ $90 °$
	Answered by MJS last updated on 23/Jun/19

	$\overset{⇀}{O P} = (\begin{matrix} 9 \\ 0 \end{matrix}) \overset{⇀}{O R} = (\begin{matrix} 10 \cos 135 ° \\ 10 \sin 135 ° \end{matrix}) = (\begin{matrix} - 5 \sqrt{2} \\ 5 \sqrt{2} \end{matrix}) \overset{⇀}{O Q} = (\begin{matrix} - 5 \sqrt{2} \\ - 5 \sqrt{2} \end{matrix})$ $their sum is (\begin{matrix} 9 - 10 \sqrt{2} \\ 0 \end{matrix}) their magnitude is 10 \sqrt{2} - 9$
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