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  4. The distance of the point whose position vector is (2 hati+ hatj- hatk) from the plane vecr ⋅( hati-2 hatj+4 hatk)=4 is

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Q. The distance of the point whose position vector is $(2 \hat{i}+\hat{j}-\hat{k})$ from the plane $\vec{r} \cdot(\hat{i}-2 \hat{j}+4 \hat{k})=4$ is

KCETKCET 2022Three Dimensional Geometry

Solution:

Distance $=\frac{|2-2-4-4|}{\sqrt{1+4+16}}=\frac{(8)}{\sqrt{21}}$