Physics - NLM Question with Solution | TestHub

Let additional force required be $\overrightarrow{\mathrm{F}}$.

Vector sum of the four forces and additional force.

$\overrightarrow{\mathrm{F}}+5\hat{i}-6\hat{i}+7\hat{j}-8\hat{j}=0$

Force required to make net acceleration zero

$\overrightarrow{\mathrm{F}}=\hat{i}+\hat{j}$

Therefore, the required force is $\left|\overrightarrow{\mathrm{F}}\right|=\sqrt{1^2+1^2}=\sqrt{2} \mathrm{N}$

Angle with $x$-axis: $\tan \theta =\frac{y \mathrm{component} }{x \mathrm{component} }=\frac{1}{1}$

Thus, $\theta =45°$