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 rdot[( hat i+2 hat j- hat k)]=4sqrt(3)dot

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

For the plane vec(r).(2hat(i)+3hat(j)+5hat(k))=3

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 equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the angel between the planes 2x+y-2x+3=0a n d vec rdot(6 hat i+3 hat j+2 hat k)=5.

The distance of a point (2,5,-3) from the plane vec r.(6 hat i-3 hat j+2 hat k)=4 is,

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)a n d vec rdot(3 hat i+ hat j+ hat k)=6.

The angle between i+j line of the intersection of the plane vec rdot( hat i+2 hat j+3 hat k)=0a n d vec rdot(3 hat i+3 hat j+ hat k)=0 is a. cos^(-1)(1/3) b. c0s^(-1)(1/(sqrt(3))) c. cos^(-1)(2/(sqrt(3))) d. none of these

Find the area of the parallelogram determined by the vectors vec a = hat i + hat j + 3 hat k , vec b = 3 hat i - 4 hat j + 5 hat k .