Explain why an acute-angle projection has positive sign

Relative to O, A,B have position vectors a,b and c is the position vector of C on AB dividing AB in the ratio 3:1. Given angle AOB is acute, show that the length d of the projection of OC onto OB is $d=\frac34|\mathbf b|+\frac{\mathbf a\cdot\mathbf b}{4|\mathbf b|}$.