Find the equation of the plane through (3, 4, -1) which is parallel to the plane ` -> r(2 hat i-3 hat j+5 hat k)+2=0.`

Explanation

Let the equation of a plane parallel to the given plane be

`vec{{r}} cdot(2_{1}^{hat{a}}-3 hat{{j}}+5 hat{{k}})={k}`


`(x vec{i}+y vec{j}+z vec{k}) cdot(2 vec{i}-3 vec{j}+5 vec{k})=k`


This passes through `(3,4,-1)`.


`therefore(3 vec{{i}}+4 vec{{j}}-vec{{k}}) cdot(2 vec{{i}}-3 vec{{j}}+5 vec{{k}})={k} `

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