Find the equation of the plane through the line of intersection of the planes ` vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0,` which is at a unit distance from the origin.

Find the Cartesian as well as vector equations of the planes through the intersection of the planes vec rdot((2 hat i+6 hat j)+12=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0 which are at a unit distance from the origin.

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 vector equation of the plane which contains the line of intersection of the plane vec rdot( hat i+2 hat j+3 hat k)-\ 4=0 and vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec rdot(5 hat i+3 hat j-\ 6 hat k)+8=0.

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 .

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 angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.