Find the Cartesian form of equation of a plane whose vector equation is : ` vec rdot((- hat i+ hat j+2 hat k)=9`

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((12 hat i-3 hat j+4 hat k)+5=0

Find the Cartesian form of the equation of the following plane: vec r=( hat i- hat j)+s( hat i+ hat j+2 hat k)+t( hat i+2 hat j+ hat k)dot

Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-7 hat k)+lambda( hat i+3 hat j+4 hat k) is parallel to the plane whose vector equation is vec rdot( hat i+ hat j- hat k)=7 . Also find the distance between them.

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 angle between the planes whose vector equations are vec r.(2 hat i+2 hat j-3 hat k)=5 and vec r.(3 hat i-3 hat j+5 hat k)=3 .

Find the Cartesian form the equation of the plane vec r=(s-2t) hat i+(3-t) hat j+(2s+t) hat kdot

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 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( hat i+ hat j+ hat k)=6 and -> rdot(2 hat i+3 hat j+4 hat k)=-5 and the point (1, 1, 1).

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.