Three Dimensional Geometry

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

→

p

=

→

SP

.

→

q

=

→

SQ

,

→

r

=

→

SR

and

→

t

=

→

ST

, then the value of |(

→

p

×

→

q

)×(

→

r

×

→

t

)| is ______.