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

• Correct answer
  A

  13, 5
• B

  12, 6
• C

  14, 4
• D

  11, 7

Solution

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 $Q$ ).

Hence, the correct answer is option: 'A'.