With two forces acting at a point, the maximum effect is obtained when their resultant is $4 \mathrm{~N}$.…

With two forces acting at a point, the maximum effect is obtained when their resultant is $4 \mathrm{~N}$. If they act at right angles, then their resultant is $3 \mathrm{~N}$. Then the forces are
  1. $(2+\sqrt{2}) N$ and $(2-\sqrt{2}) N$
  2. $(2+\sqrt{3}) \mathrm{N}$ and $(2-\sqrt{3}) \mathrm{N}$
  3. $\left(2+\frac{1}{2} \sqrt{2}\right) \mathrm{N}$ and $\left(2-\frac{1}{2} \sqrt{2}\right) \mathrm{N}$
  4. $\left(2+\frac{1}{2} \sqrt{3}\right) \mathrm{N}$ and $\left(2-\frac{1}{2} \sqrt{3}\right) \mathrm{N}$

Solution

$P+Q=4, P^2+Q^2=9 \Rightarrow P=\left(2+\frac{1}{2} \sqrt{2}\right) N$ and $Q=\left(2-\frac{1}{2} \sqrt{2}\right) N$

Asked in: JEE Main 2004

Practice more Vectors questions on Aicharya