Question

Assertion :STATEMENT-$1$ : $[\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}\overrightarrow{a}\times \overrightarrow{b}]=0$ Reason: STATEMENT-$2$ : If $\overrightarrow{p},\overrightarrow{q},\overrightarrow{r}$ are linearly dependent vectors then they are coplanar

• A. Statement-$1$ is True, Statement-$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$
• B. Statement-$1$ is True, Statement-$2$ is True; Statement-$2$ is Not a correct explanation for Statement-$1$
• C. Statement-$1$ is True, Statement-$2$ is False
• D. Statement-$1$ is False, Statement-$2$ is True

Answer 1

The correct option is D Statement-$1$ is False, Statement-$2$ is True

$[\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}\overrightarrow{a}\times \overrightarrow{b}]=[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}{]}^2$

but if $\left[\overrightarrow{p}\overrightarrow{q}\overrightarrow{r}\right]=0$

i.e $\overrightarrow{p},\overrightarrow{q},\overrightarrow{r}$ are lineraly dependent vectors so they are coplanar