Find the equation the plane which contain the line of intersection of the planes` vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0` and which is perpendicular to the plane ` vec r(5 hat i+3 hat j-6 hat k)+8=0` .

Explanation

Here is the solution :

` vecr cdot( hat i+2 hat j+3 hat k)-4=0....1`

`vecr cdot(2 hat i+ hat j- hat k)+5=0....2`

The equations of the plane passing through the line intersection of the plane given in equation (1) and equation (2) is


`[vecr cdot( hat i+2 hat j+3 hat k)-4] lambda [vecr cdot(2 hat i+ hat j- hat k)+5] = 0`


=`vecr.[(2λ+1)
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