Arrange the vectors subtractions so that their magnitudes are in decreasing order. If the two vectors $\overrightarrow{\mathrm{A}} \mathrm{and} \overrightarrow{\mathrm{B}}$ are acting at an angle $\left(\right|\overrightarrow{\mathrm{A}}|>|\overrightarrow{\mathrm{B}}\left|\right)$.
a) 60^o b) 90^o c) 180^o d) 120^o

a) $\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2-2\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|\cos {60}^{\circ }=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2-\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|$

b) $\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2-2\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|\cos {90}^{\circ }=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2$

c) $\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2-2\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|\cos {180}^{\circ }=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2+2\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|$

d) $\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2-2\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|\cos {120}^{\circ }=|\overrightarrow{\mathrm{A}}{|}^2+|\overrightarrow{\mathrm{B}}{|}^2+\left|\overrightarrow{\mathrm{A}}\right|\left|\overrightarrow{\mathrm{B}}\right|$

$\Rightarrow \mathrm{c}>\mathrm{d}>\mathrm{b}>\mathrm{a}$