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 the plane passing through the line of intersection of the planes vec r*(hat i+hat j+hat k)=1 and vec r*(2hat i+3hat j-hat k)+4=0 and parallel to x-axis.

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

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

Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes vec rdot( (hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

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

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 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 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 vector equation of plane passing through thein tersection of planes vec r*(hat i+3hat j-hat k))=5 and vec r*(2hat i-hat j+hat k)=3 and point (2,1,-2)