In a right angle $\triangle \mathrm{ABC}, \angle \mathrm{A}=90^{\circ}$ and sides a, b, c are respectively,…

In a right angle $\triangle \mathrm{ABC}, \angle \mathrm{A}=90^{\circ}$ and sides a, b, c are respectively, $5 \mathrm{~cm}, 4 \mathrm{~cm}$ and $3 \mathrm{~cm}$. If a force $\vec{F}$ has moments 0,9 and 16 in $N$ cm. units respectively about vertices $A, B$ and $C$, then magnitude of $\vec{F}$ is
  1. 3
  2. 4
  3. 5
  4. 9

Solution

$\mathrm{F} \cdot 3 \sin \theta=9$ $\mathrm{~F} \cdot 4 \cos \theta=16$ $\Rightarrow \mathrm{F}=5$

Asked in: JEE Main 2004

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