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 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.

Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes -> rdot( hat i- hat j+2 hat k)=5\ a n d\ -> rdot(3 hat i+ hat j+ hat k)=6.

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 is parallel to the lines vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1"" and is passing through the point (0,1,-1 ).

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

Find the equation of the plane passing through the line of intersection of the planes vec(r)*(2hat(i)-7hat(j)+4hat(k))=3and3x-5y+4z+11=0," and the point "(-2,1,3).

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

Find the point where line which passes through point (1,2,3) and is parallel to line vec r= hat i+ hat j+2 hat k+lambda( hat i-2 hat j+3 hat k) meets the xy-plane.