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Find the cartesian equation of the plane passing through the intersection of the planes and and at…

Mathematics20184 marksShort answer
Find the cartesian equation of the plane passing through the intersection of the planes $\vec{r} \cdot (2\hat{\imath} + 6\hat{\jmath}) + 12 = 0$ and $3x - y + 4z = 0$ and at a unit distance from origin.

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Three-dimensional Geometry

From ISC 2018 Specimen Mathematics Paper 1, question 17(b).