Find the equation of the plane passing through `(a ,b ,c)` and parallel to the plane ` vec rdot( hat i+ hat j+ hat k)=2.`

Explanation

We know, Any plane to parallel to the planer. `(hat{i}+hat{j}+hat{k})=2` is for the form
`vec{{r}} cdot(hat{{i}}+hat{{j}}+hat{{k}})=lambda ldots ldots(1)`

The plane passes through the point (a, b, c).
So, the position vector r of
this point is `hat{a}+b hat{j}+c hat{k}.`

Therefore, equation (1) becomes

`(hat{a}+b hat{j}+c hat{k}) cdot(hat{1}+hat{j}+hat{k})=lambda `

`Rightarrow a+b+c=lambda`


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