Let p, q, r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies equation \[\mathbf{p}\times \{(\mathbf{x}-\mathbf{q})\times \mathbf{p}\}+\mathbf{q}\times \{(\mathbf{x}-\mathbf{r})\times \mathbf{q}\}+\mathbf{r}\times \{(\mathbf{x}-\mathbf{p})\times \mathbf{r}\}=0,\] then x is given by [IIT 1997 Cancelled]

• A. \[\frac{1}{2}\,(\mathbf{p}+\mathbf{q}-2\mathbf{r})\]         
• B. \[\frac{1}{2}(\mathbf{p}+\mathbf{q}+\mathbf{r})\]
• C. \[\frac{1}{3}(\mathbf{p}+\mathbf{q}+\mathbf{r})\]
• D. \[\frac{1}{3}(2\mathbf{p}+\mathbf{q}-\mathbf{r})\]