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

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 unit vector perpendicular to the plane vec rdot(2 hat i+ hat j+2 hat k)=5.

Find the equation of the plane which contains the line of intersection of the planes vec r . ( hat i+2 hat j+3 hat k)-4=0,\ vec r . (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 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 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 distance of a point (2, 5, 3) from the plane vecr.(6 hat i-3 hat j+2 hat k)=4 .

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

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Show that the equation of the planes are perpendicular to each other. vecr.(2 hat i- hat j+3 hat k)=5 and vecr.(2 hat i- 2 hat j - 2 hat k)=5