Let veca=hati+5 hat j+alpha hat k, vecb=...

Let `veca=hati+5 hat j+alpha hat k`, `vecb=hati+3hatj+betahatk` and `vec c=-hati+2hatj-3hatk` be three vectors such that, `|vecbxxvec c|=5sqrt(3)` and `veca` is perpendicular to `vecb`. Then the greatest amongst the values of `|veca|^(2)` is ____________.

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