Question 21

Let PQR be a triangle such that $$\overrightarrow{PQ}=-2\widehat{i}-\widehat{j}+2\widehat{k}$$ and $$\overrightarrow{PR}=a\widehat{i}+b\widehat{j}-4\widehat{k},a,b \in Z$$. Let S be the point on QR, which is equidistant from the lines PQ and PR. If $$|\overrightarrow{PR}|=9$$ and $$\overrightarrow{PS}=\widehat{i}-7\widehat{j}+2\widehat{k}$$, then the value of 3a - 4b is_______


Correct Answer: 37

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