Find the radius of the circular section in which the sphere `| vec r|=5` is cut by the plane ` vec rdot( hat i+ hat j+ hat k)=3sqrt(3.)`

Find the radius of the circular section of the sphere |vec r|=5 by the plane vec r*(hat i+2hat j-hat k)=4sqrt(3)

Write the plane vec rdot((2 hat i+3 hat j-6 hat k)=14 in normal form.

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

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 vector and Cartesian equations 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 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 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 which contains the line of intersection of the planes vec r*(hat i+2hat j+3hat k)-4=0,vec r*(2hat i+hat j-hat k)+5=0 and which is perpendicular to the plane

Find the equation of the plane through the point 2 hat i+ hat j- hat k and passing through the line of intersection of the plane vec rdot(( hat i+3 hat j- hat k)=0\ a n d\ vec rdot(( hat j+2 hat k)=0.