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Consider the cube in the first octant wi...

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 `vec(p)=vec(SP), vec(q)=vec(SQ), vec(r)=vec(SR)` and `vec(t)=vec(ST)` then the value of `|(vec(p)xxvec(q))xx(vec(r)xx(vec(t))| is `

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