Question

Please help i can't find the answers anywhere ​

Answer 1

(i) $a = \frac{ - 1}{3} ,b = \frac{1}{2}$

$\large\bold{\underline{\underline{To\:verify:-}}}$

:⟼  $|a \times b| = |a| \times |b|$

$\large\bold{\underline{\underline{Solution:-}}}$

:⟼  $| \frac{ - 1}{3} \times \frac{1}{2} | = | \frac{ - 1}{3} | \times | \frac{1}{2} |$

:⟼  $| \frac{ - 1 \times 1}{3 \times 2} | = \frac{1}{3} \times \frac{1}{2}$

:⟼  $| \frac{ - 1}{6} | = \frac{1}{6}$

:⟼  $\frac{1}{6} = \frac{1}{6}$

:⟼  L. H. S. = R. H. S.

$\boxed{ Hence\:verified. }$

(ii) $a = \frac{ - 1}{7} ,b = \frac{ - 3}{4}$

$\large\bold{\underline{\underline{Solution:-}}}$

:⟼  $| \frac{ - 1}{7} \times \frac{ - 3}{4} | = | \frac{ - 1}{7} | \times | \frac{ - 3}{4} |$

:⟼  $| \frac{ - 1 \times - 3}{7 \times 4} | = \frac{ 1}{7} \times \frac{3}{4}$

:⟼  $\frac{3}{28} = \frac{3}{28}$

:⟼  L. H. S. = R. H. S.

$\boxed{ Hence\:verified. }$

(iii) $a = \frac{5}{9} ,b = \frac{2}{3}$

$\large\bold{\underline{\underline{Solution:-}}}$

:⟼  $| \frac{5}{9} \times \frac{2}{3} | = | \frac{5}{9} | \times | \frac{2}{3} |$

:⟼  $| \frac{10}{27} | = \frac{5}{9} \times \frac{2}{3}$

:⟼  $\frac{10}{27} = \frac{10}{27}$

:⟼  L. H. S. = R. H. S.

$\boxed{ Hence\:verified. }$

$\large\mathfrak{{\pmb{\underline{\red{Tornado77 }}{\red{❦}}}}}$