Let ` vec n` be a vector of magnitude `2sqrt(3)` such that it makes equal acute angles with the coordinate axes. Find the vector and Cartesian forms of the equation of a plane passing through `(1,-1,2)` and normal to ` vec ndot`

Explanation

Let the acute angle be `cosalpha`

since angle are equal so,

directional ratio`=cos^2alpha+cos^2alpha+cos^2alpha=1 `

`=cosalpha=1/(sqrt3)`


thus,

`vecn=2sqrt3(cosalpha hati+cosalpha hatj+cosalpha hatk)`

`vecn=2sqrt3(1/(sqrt3)hati+1/(sqrt3) hatj+1/(sqrt3) hatk)`

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