Consider a plane II: \( \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})=5 \), a line \( L_{1} \) : \( \... VIDEO
Consider a plane II: \( \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})=5 \), a line \( L_{1} \) : \( \vec{r}=3 \hat{i}-\hat{j}+2 \hat{k}+\lambda(2 \hat{i}-3 \hat{j}-\hat{k}) \) where \( \lambda \in R \) and a point \( A(3 \), \( -4,1) \). The line \( L_{1} \) intersects plane II at \( Q \) and \( x y \)-plane at \( R \). If the volume of tetrahedron OAQR ( \( O \) is origin) is \( \frac{m}{n} \) where \( m \) and \( n \) are relatively prime positive integers, then find \( (3 m-5 n) \)https://bit.ly/YTAI_PWAP https://www.pw.live
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