Mathematics - Vector Question with Solution | TestHub

Consider the cube in the first octant with sides $\mathrm{OP},\mathrm{OQ}$ and OR of length 1 , along the x axis, $y$-axis and $z$-axis, respectively, where $\mathrm{O}(0,0,0)$ is the origin. Let $\mathrm{S}\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If $\vec{p}=\overrightarrow{SP},\vec{q}=\overrightarrow{SQ},\vec{r}=\overrightarrow{SR}$ and $\vec{t}=\overrightarrow{ST}$, then the value of $2|(\overrightarrow{\mathrm{p}}\times \overrightarrow{\mathrm{q}})\times (\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{t}})|$ is $\_\_\_\_$ .