Let `P=0` be the plane,passing through the line of intersection of the planes `x+y+2z-4=0 & 2x-y-5z+1=0` & parallel to the vector `(hat i+hat j+hat k)` Then distance of `P=0` from origin is

Let P=0 be the plane,passing through the line of intersection of the planes x+y+2z-4=0&2x-y-5z+1=0 & parallel to the vector (i+j+hat k) .Then distance of P=0 from origin is

Let P = 0 be the plane, passing through the line of intersection of the planes x + y + 2z - 4 = 0 & 2x - y - 5z + 1 = 0 & parallel to the vector (i+j+k). Then distance of P = 0 from origin is

If the z -intercept of the plane which is passing through the intersection of the planes x+2y+3z+5=0 and 2x-5y+4z+7=0 and parallel to the line vec r=2hat i+5hat j+hat k+t(hat i+hat j+2hat k) is lambda then [|lambda|] equals (where t in R ) (where [.] denotes greatest integer function)

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 equation of the plane, passing through the line of intersection of the planes: vec r*(2hat i+3hat j-4hat k)+5=0 and vec r*(hat i-5hat j+7hat k)+2=0 and intersecting y-axis at (0,3)

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 passing through the line of intersection of the planes vec r*(hat i+hat j+hat k)=1 and vec r*(2hat i+3hat j-hat k)+4=0 and parallel to x-axis.

Find an equation for the plane through P_(0)=(1, 0, 1) and passing through the line of intersection of the planes x +y - 2z = 1 and x + 3y - z = 4 .

A line passing through the point A(1,-1,-1) and is parallel to the vector (3hat i-2hat j+3hat k) .The shortest distance of the point (0,2,1) from the line is

Find the cartesian as well as vector equation of the planes through the intersection of the planes vec r*(2hat i+6hat j)+12=0 and vec r*(3hat i-hat j+4hat k)=0, which are at unit distance from the origin.