Let O be the origin. Let vec(OP) = x hat...

Let O be the origin. Let `vec(OP) = x hati+y hati-hatk and vec(OQ) = -hati+2hatj+3x hatk, x y in R , x gt 0`, be such that `|vec(PQ)|=sqrt(20)` and the vector `vec(OP)` is perpendicular to `vec(OQ)`. If `vec(OR)=3hati+zhatj-7hatk, z in R`, is coplanar with `vec(OP) and vec(OQ)`, then the value of `x^(2)+y^(2)+z^(2)` is equal to :

A

1

B

7

C

9

D

2

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