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Find the equation of the plane through the intersection of the planes

Question:

Find the equation of the plane through the intersection of the planes $\vec{r} \cdot(\hat{i}+3 \hat{j})-6=0$ and $\vec{r} \cdot(3 \hat{i}-\hat{j}-4 \hat{k})=0$, whose perpendicular distance from origin is unity.

Solution:

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