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Let a and b positive real numbers. suppo...

Let a and b positive real numbers. suppose `bar(PQ)`=`(a)bar(i)`+`(b)bar(j)` and `bar(PS)=(a)bar(i)-(b)bar(j)` are adjacent sides parallelogram. Let `bar(u)` and `bar(v)` be the projection vectors of `bar(omega)=bar(i)+bar(j)` along `bar(PQ)` and `bar(PS)` respectively. If `|bar(u)|+|bar(v)|=|bar(omega)|`and if area of the parallelogram PQRS is 8 then a+b=

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