The forces F_1 = (2i + bj) N, F_2 = (−i + 2j) N and F_3 = (ai −4j)N act through the points with position vectors r_1 = (i + 3j)m ,r_2 =(xi + 5j) m and r_3 =(−i + j)m respectively . Given that this system of forces is equivalent to a couple of magnitude 12 N m, find a) the valueof the scalars a and b b) the possible values of the scalar x.


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Question Number 79738 by Rio Michael last updated on 27/Jan/20

$T h e f o r c e s F_{1} = (2 i + b j) N, F_{2} = (- i + 2 j) N$ $a n d F_{3} = (a i - 4 j) N a c t t h r o u g h t h e p o i n t s w i t h$ $p o s i t i o n v e c t o r s r_{1} = (i + 3 j) m, r_{2} = (x i + 5 j) m$ $a n d r_{3} = (- i + j) m r e s p e c t i v e l y .$ $G i v e n t h a t t h i s s y s t e m o f f o r c e s i s e q u i v a l e n t t o a c o u p l e$ $o f m a g n i t u d e 12 N m, f i n d$ $a) t h e v a l u e o f t h e s c a l a r s a a n d b$ $b) t h e p o s s i b l e v a l u e s o f t h e s c a l a r x .$
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