Question

If $\overline{a},\overline{b}$ are vectors of length a, b, then ${\left(\frac{\overline{a}}{a^2}-\frac{\overline{b}}{b^2}\right)}^2=$

• A. ${\left(\frac{\overline{a}+\overline{b}}{ab}\right)}^2$
• B. ${\left(\frac{\overline{a}-\overline{b}}{ab}\right)}^2$
• C. $\left(\frac{\overline{a}+\overline{b}}{ab}\right)$
• D. $\left(\frac{\overline{a}-\overline{b}}{ab}\right)$

Answer 1

The correct option is B ${\left(\frac{\overline{a}-\overline{b}}{ab}\right)}^2$

${(\frac{\overline{a}}{{\left|\overline{a}\right|}^2}-\frac{\overline{b}}{{\left|\overline{b}\right|}^2})}^2⟹\frac{{\left|\overline{a}\right|}^2}{{\left|\overline{a}\right|}^4}+\frac{{\left|\overline{b}\right|}^2}{{\left|\overline{b}\right|}^4}-\frac{2\overline{a}.\overline{b}}{{\left|\overline{a}\right|}^2.{\left|\overline{b}\right|}^2}⟹\frac{1}{{\left|\overline{a}\right|}^2}+\frac{1}{{\left|\overline{b}\right|}^2}-\frac{2\overline{a}.\overline{b}}{{\left|\overline{a}\right|}^2.{\left|\overline{b}\right|}^2}⟹\frac{{\left|\overline{b}\right|}^2+{\left|\overline{a}\right|}^2-2\overline{a}.\overline{b}}{{\left|\overline{a}\right|}^2.{\left|\overline{b}\right|}^2}⟹\frac{{\left(|\overline{a}-\overline{b}|\right)}^2}{{\left|\overline{a}\right|}^2.{\left|\overline{b}\right|}^2}⟹\left|\frac{{|\overline{a}-\overline{b}|}^2}{{(\left|\overline{a}\right|.\left|\overline{b}\right|)}^2}\right|⟹{\left|\frac{\overline{a}-\overline{b}}{\left|\overline{a}\right|\left|\overline{b}\right|}\right|}^2\therefore B)Ans.$