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Let the position vectors of two points P...

Let the position vectors of two points P and Q be `3 hati - hatj + 2 hatk and hati + 2 hatj -4 hatk,` respectively. Let Rand 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 `vec(TA)` is perpendicular to both `vec(PR) and vec(QS)` and the length of vector `vec(TA) is sqrt5` units, then the modulus of a position vector of A, is :

A

`sqrt5`

B

`sqrt (171)`

C

`sqrt (227)`

D

`sqrt (482)`

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