The distance of the point $2 i + j - k$ from the plane $r (i - 2 j + 4 k) = 9$ is

\frac{13}{\sqrt{21}}

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\frac{3}{\sqrt{21}}

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\frac{13}{21}

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\frac{13}{3 \sqrt{21}}

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Solution

The correct option is B $\frac{3}{\sqrt{21}}$
we have formula,

Distance $= \frac{| a \cdot n - d |}{n}$

Given,

$a = 2 i + j - k, n = i - 2 j + 4 k$ and $d = 9$

$= \frac{| (2 i + j - k) \cdot (i - 2 j + 4 k) - 9 |}{i - 2 j + 4 k}$

$= \frac{| 2 - 2 - 4 - 9 |}{\sqrt{21}}$

$= \frac{13}{\sqrt{21}}$

Suggest Corrections

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