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If $O (0, 0, 0), A (2, 3, - 4), B (3, 4, - 5)$ and $\cos ∠ O A B = \sqrt{\frac{p + 2}{Q - 3}}$ , then $\sqrt{p (Q + 4)} =$

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Correct option is C

The given points are O0,0,0, A2,3,−4, B3,4,−5Hence, the vectors are AO¯=−2i−3j+4k,AB¯=i+j−k cos∠OAB=−2−3−44+9+161+1+1=9293=2729 Therefore, p=25,Q=32 and 2532+4=5⋅6=30

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If O0,0,0, A2,3,−4, B3,4,−5 and cos∠OAB=p+2Q−3, then pQ+4=

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If $O (0, 0, 0), A (2, 3, - 4), B (3, 4, - 5)$ and $\cos ∠ O A B = \sqrt{\frac{p + 2}{Q - 3}}$ , then $\sqrt{p (Q + 4)} =$