Given that vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ from a triangle such that $\overrightarrow{a} = \overrightarrow{b}+ \overrightarrow{c}$. Find p,q,r,s such that area of triangle is $5 \sqrt 6$ where $\overrightarrow{a} = p \hat i +q \hat j +r \hat k$ ,$\overrightarrow{b} = s \hat i +3 \hat j +4 \hat k$ and $\overrightarrow{c} = 3 \hat i + \hat j -2 \hat k$

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