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The line vec r=2hat i-2hat j+5hat k+lamb...

The line `vec r=2hat i-2hat j+5hat k+lambda(hat i-3hat j+2hat k)` intersects the plane `2x-3y+4z=163` at `P` and intersects the `YZ` plane at `Q.` If the distance `PQ` is `9sqrt(a)` where `a in N` then `a` equals

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