JEE Advanced 2018 Paper 2 Mathematics Q13

Mathematics

Problem

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0, 0, 0) is the origin. Let S(1/2, 1/2, 1/2) 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 p⃗\vec{p} = SP⃗\vec{P}, q⃗\vec{q} = SQ⃗\vec{Q}, r⃗\vec{r} = SR⃗\vec{R} and t⃗\vec{t} = ST⃗\vec{T}, then the value of |(p⃗\vec{p} × q⃗\vec{q}) × (r⃗\vec{r} × t⃗\vec{t})| is _____.

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