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

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

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

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

A unit vector parallel to the intersection of the planes vec rdot( hat i- hat j+ hat k)=5a n d vec rdot(2 hat i+ hat j-3 hat k)=4 a. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) b. (-2 hat i+5 hat j-3 hat k)/(sqrt(38)) c. (2 hat i+5 hat j-3 hat k)/(sqrt(38)) d. (-2 hat i-5 hat j-3 hat k)/(sqrt(38))

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.

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.

A vector parallel to the line of intersection of the planes vec r=dot(3 hat i- hat j+ hat k)=1\ a n d\ vec rdot(( hat i+4 hat j-2 hat k)=2 is a. -2 hat i+7 hat j+13 hat k b. 2 hat i+7 hat j-13 hat k c. -2i-7j+13 k d. 2i+7j+13 k

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 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