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Find the vector equation of the plane passing through the point having position vector i + j + k and perpendicular to the vector 4i + 5j + 6k.

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The vector equation of the plane passing through the point A(\(\bar{a}\)) and perpendicular to the vector \(\bar{n}\) is

∴ the vector equation of the required plane is \(\bar{r}.(4\hat{i} + 5\hat{j} + 6\hat{k})\) = 15.

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