Question

$\overline{a}+2\overline{b}+3\overline{c}=0$ and $\overline{a}\times \overline{b}+\overline{b}\times \overline{c}+\overline{c}\times \overline{a}=l(\overline{b}\times \overline{c})$, then $l=$

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

Let $\overline{a}+2\overline{b}+3\overline{c}=0$ ..........(1)

$\therefore \overline{a}\times \overline{b}+\overline{b}\times \overline{c}+\overline{c}\times \overline{a}$

$=(-2\overline{b}-3\overline{c})\times \overline{b}+\overline{b}\times \overline{c}+\overline{c}\times (-2\overline{b}-3\overline{c})$

$=-2\overline{b}\times \overline{b}-3\overline{c}\times \overline{b}+\overline{b}\times \overline{c}-2\overline{c}\times \overline{b}-3\overline{c}\times \overline{c}$

$=3\overline{b}\times \overline{c}+\overline{b}\times \overline{c}+2\overline{b}\times \overline{c}=6\overline{b}\times \overline{c}$,

Since $\overline{b}\times \overline{b}=0$ and $\overline{b}\times \overline{c}=-\overline{c}\times \overline{b}$