Let vecx be a vector in the plane contai...

Let `vecx` be a vector in the plane containing vectors `veca=2hati-hatj+hatk and vecb=hati+2hatj-hatk`. If the vector `vecx` is perpendicular to `(3hati+2hatj-hatk)` and its projection on `veca` is `(17sqrt(6))/(2)`, then the value of `|vecx|^(2)` is equal to __________.

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