Question

$\overline{a}\times \{\overline{b}\times (\overline{c}\times \overline{d}\left)\right\}$ is equal to

• A. $(\overline{b}\cdot \overline{a})(\overline{c}\times \overline{d})-(\overline{b}\cdot \overline{c})(\overline{a}\times \overline{d})$
• B. $(\overline{b}\cdot \overline{c})(\overline{a}\times \overline{d})-(\overline{b}\cdot \overline{a})(\overline{b}\times \overline{d})$
• C. $(\overline{b}\cdot \overline{d})(\overline{a}\times \overline{c})-(\overline{b}\cdot \overline{c})(\overline{a}\times \overline{d})$
• D. $(\overline{b}\cdot \overline{a})(\overline{b}\times \overline{a})-(\overline{c}\cdot \overline{d})(\overline{c}\times \overline{d})$

Answer 1

Answer: (C)

$(\overline{b}\cdot \overline{d})(\overline{a}\times \overline{c})-(\overline{b}\cdot \overline{c})(\overline{a}\times \overline{d})$

$\overline{b}\times (\overline{c}\times \overline{d})=(\overline{b}.\overline{d})\overline{c}-(\overline{b}.\overline{c})\overline{d}$
So, $\overline{a}\times \{\overline{b}\times (\overline{c}\times \overline{d}\left)\right\}=\overline{a}\times \left[\right(\overline{b}.\overline{d})\overline{c}-(\overline{b}.\overline{c}\left)\overline{d}\right]$
$=(\overline{b}.\overline{d})(\overline{a}\times \overline{c})-(\overline{b}.\overline{c})(\overline{a}\times \overline{d})$