A parallelogram is constructed on 5a→+2b→ and a→−3b→ as adjacent sides, where |a→|=22 and |b→|=3 & angle between a→&b→ is π4 . If the magnitude of longer diagonal is αβγ where αβγ is three digit number then α+β−γ is equal to

Given that |a→|=22,|b→|=3 and angle between a→ and b→ is π4 The diagonals of the parallelogram are p→=5a→+2b→+a→−3b→=6a→−b→ and q→=4a→+5b→|p→|=|6→a→−b→|=36|a→|2+|b→|2−12(a→⋅b→)=36×8+9−12×22×3×12=15 And |q→|=|4a→+5b→|=16|a→|2+25|b→|+40(a·→b→)=16×8+25×9+40×22×3×12=593∴ Magnitude of longer diagonal =593=αβγ (given) ∴α+β−γ=5+9−3=11