If ` vec n` is a vector of magnitude `sqrt(3)` and is equally inclined with an acute angle with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane which passes through (2, 1, -1) and is normal to ` vec n` .

Explanation

Let `\alpha, \beta, \gamma` angles of `\overline{{n}}`

Given angels are equal So:` \alpha=\beta=\gamma`


ie:` \cos \alpha=\cos \beta=\cos \gamma`


So direction cosines` \Rightarrow 1={m}={n} \Rightarrow 1=1=1`


As we know` {l}^{2}+{m}^{2}+{n}^{2}={n} \Rightarrow 8 {l}^{2}=1`

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