Find the equation of the plane through the point `2 hat i+ hat j- hat k` and passing through the line of intersection of the plane ` vec rdot(( hat i+3 hat j- hat k)=0\ a n d\ vec rdot(( hat j+2 hat k)=0.`

Explanation

Equation of pairing through the intersection of planes `vec r * vec n_1 = d_1` & `vec r * vec n_2=d_2` is


`Rightarrow vec r*(vec n_1 + lambda vec n_2) = d_1 + lambda * d_2`


Using the above formula for the plane 1


`Rightarrow vec r * (hat I + 3 hat j – hat k) = 0` ; `vec n_1 = hat i + 3 hat j – hat k` ; `d_1=0`


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