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

Explanation

As we know that any plane which is parallel to the plane `r
.(i+j​+k)=2` is for the form

r
.(i+j+k)=λ.....(1)

As this plane passes through the point (a,b,c).
Therefore, the position vector r.
of this point is ai+bj​+ck
Therefore, equation (1) becomes

(ai+bj+ck).(i+j​+k)=λ

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