question_answer

If \[\overrightarrow{p,}\]\[\overrightarrow{q,}\]\[\overrightarrow{r}\]are three mutually perpendicular vectors of the same magnitude. If a vector\[\overrightarrow{x}\] satisfies the equation, \[\overrightarrow{p}\times \left[ (\overrightarrow{x}-\overrightarrow{q})\times \overrightarrow{p} \right]+\overrightarrow{q}\times \left[ (\overrightarrow{x}-\overrightarrow{r)}\times \overrightarrow{q} \right]+\overrightarrow{r}\times \left[ (\overrightarrow{x}-\overrightarrow{p})\times \overrightarrow{r} \right]=0\]then \[\overrightarrow{x}\]is given by

A)  \[\frac{1}{2}\,\,(\overrightarrow{p}+\overrightarrow{q}-2\overrightarrow{r})\]         

B)  \[\frac{1}{2}\,\,(\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r})\]

C)  \[\frac{1}{3}\,\,(\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r})\]                     

D)  \[\frac{1}{3}\,\,(2\overrightarrow{p}+\overrightarrow{q}-\overrightarrow{r})\]            

E)             None of these