Find the vector equation of the plane passing through three points with position vectors \( \hat...

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Find the vector equation of the plane passing through three points with position vectors \( \hat{i}+\hat{j}-2 \hat{k}, 2 \hat{i}-\hat{j}+\hat{k} \) and \( \hat{i}+2 \hat{j}+\hat{k} \). Also find the co-ordinates of the point of intersection of this plane and the line \( \vec{r}=3 \hat{i}-\hat{j}-\hat{k}+\lambda(2 \hat{i}-2 \hat{j}+\hat{k}) \)
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