The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are

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Aicharya · Accepted Answer

Let two forces be $P$ and $Q$. Given $P+Q=18$ and $P \hat{a}+Q \hat{b}=12 \hat{c} \Rightarrow P \hat{a}-12 \hat{c}=\bar{Q} \hat{b}$ $ \begin{aligned} & \Rightarrow P^2+144=Q^2=(18-P)^2 ; \Rightarrow P^2+144=324-36 P+P^2 \\ & \Rightarrow 36 P=180 \Rightarrow P=5 \text { and } Q=13 \end{aligned} $ (where $\vec{a}$ and $\vec{b}$ are unit vectors along $P$ and $Q$ )

The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N.…

Solution