The distance of the point 2î + ĵ - k̂ from the plane r⃗ · (î - 2ĵ + 4k̂) = 9 will be:

The distance of the point $2\hat{i} + \hat{j} - \hat{k}$ from the plane $\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 9$ will be:

(a)$13$
(b)$\frac{13}{\sqrt{21}}$
(c)$21$
(d)$\frac{21}{\sqrt{13}}$

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Answer

Correct option: (b)

Answer: (b) $\frac{13}{\sqrt{21}}$ Distance $= \frac{|\vec{a}\cdot\vec{n} - d|}{|\vec{n}|} = \frac{|(2)(1) + (1)(-2) + (-1)(4) - 9|}{\sqrt{1+4+16}} = \frac{13}{\sqrt{21}}$.