Question

Two force are such that the sum of their magnitude is 18 N and their resultant is perpendicular to the smaller force and the magnitude of resultant is 12 N. Then the magnitude of the force are

Answer 1

Let the force of smaller magnitude be A and force of larger magnitude be B

Given that resultant force makes an angle 98 with the smaller force

$B^2=R^2+A^2$

$R^2=B^2-A^2={12}^2=144$

$\therefore A+B=18$ $B=18-A$

$(18-A{)}^2-A^2=144$

$324-36A+A^2-A^2=144=36A=324-144$

$=180$

$\therefore A=\frac{180}{36}=5$

$\therefore B=18-A$

$=18-5=13$

$\therefore$ magnitude in Two vectors are $5$ and $13$