Скачать или смотреть Consider the cube in the first octant with sides OP, OQ and OR of l...

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the \( \mathrm{x} \)-axis, \( \mathrm{y} \)-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 \( \mathrm{T} \) be
\( \mathrm{P} \) the vertex of the cube opposite to the origin \( \mathrm{O} \) such that \( \mathrm{S} \) lies on the diagonal \( \mathrm{OT} \). If \( \overrightarrow{\mathrm{p}}=\overrightarrow{\mathrm{SP}} \),

W \( \overrightarrow{\mathrm{q}}=\overrightarrow{\mathrm{SQ}}, \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{SR}} \) and \( \overrightarrow{\mathrm{t}}=\overrightarrow{\mathrm{ST}} \), then the value of \( |(\overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{q}}) \times(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{t}})| \) is
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