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(12,12,12) 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 →p=−→SP,→q=−−→SQ,→r=−−→SR and →t=−→ST, then the value of |(→p×→q)×(→r×→t)| is

Consider the cube in the first octant with sides OP,OQ and OR of lengt

1.	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(12,12,12) 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 →p=−→SP,→q=−−→SQ,→r=−−→SR and →t=−→ST, then the value of \|(→p×→q)×(→r×→t)\| is
Answer» Consider the cube in the first octant with sides $O P, O Q$ and $O R$ of length $1,$ along the x-axis, y-axis and z-axis, respectively, where $O (0, 0, 0)$ is the origin. Let $S (\frac{1}{2}, \frac{1}{2}, \frac{1}{2})$ 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 $O T .$ If $\to p = - \to S P, \to q = - - \to S Q, \to r = - - \to S R$ and $\to t = - \to S T,$ then the value of $\| (\to p \times \to q) \times (\to r \times \to t) \|$ is