Find the equation of the plane passing through the intersection of the planes ` vec r .(2 hat i+ hat j+3 hat k)=7, vec r.(2 hat i+5 hat j+3 hat k)=9` the point `(2,1,3)dot`

Find the equation of the plane passing through the intersection of the planes vec rdot( hat i+ hat j+ hat k)=\ 6,\ vec rdot\ \ (2 hat i+3 hat j+4 hat k)=\ -5 and the point (1,1,1).

Find the vector equation of the plane passing through the intersection of the planes -> rdot(2 hat i+2 hat j-3 hat k)=7, -> rdot(2 hat i+5 hat j+3 hat k)=9 and through the point (2, 1, 3).

Find the vector and cartesian equations of the plane passing through the line of intersection of the planes vec r (2 hat i+2 hat j-3 hat k)=7,vec r (2 hat i+5 hat j+3 hat k)=9 such that the intercepts made by the plane on x-axis and z-axis are equal.

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

Find the equation of a plane through the intersection of the planes vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3 and passing through the point (2,1,-2)dot

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

Find the equation of the plane which contains the line of intersection of the planes vec r . ( hat i+2 hat j+3 hat k)-4=0,\ vec r . (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.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0 .

Find the equation of plane passing through the point hat i+ hat j+ hat k and parallel to the plane vecr.(2 hat i- hat j+2 hat k)=5.