Intersection Lines Perpendicular Vector 3D

Let the position vectors of two points P and Q be 3

∧

i

−

∧

j

+2

∧

k

and

∧

i

+2

∧

j

−4

∧

k

, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are (4,−1,2) and (−2,1,−2), respectively. Let lines PR and QS intersect at T. If the vector TA is perpendicular to both PR and QS and the length of vector TA is √5 units, then the modulus of a position vector of A is