Find the magnitude of two forces having their resultant 12N which is perpendicular to the smaller force and their greatest resultant is 18N.

Let the two vectors be a and b.We get the greatest resultant when the angle between the two vectors is 0°.So a+b=18 Let the resultant be perpendicular to a therefore a + component of b along a is zero. If the angle between a and b is x, then b.cosx + a=0. --------iBy drawing the figure of a,b and their resultant we can show that b.cos(x-90°)=12 or b.sinx=12. --------iiBy squaring the equation ii we get b.cosx =√[b^2-144]From ib.cosx + a =0 or√[b^2-144] + 18-b=0orb^2-144=[18-b]^2Solving the equation we get b=5. .°. a = 18-5=13