Find the vector equation of a plane passing through the point having position vector `2hati+hatj+hatk` and perpendicular to the vector: `4hati-2hatj+3hatk`.

Find the vector equation of a line passing through the point with position vector (2hati-3hatj-5hatk) and perpendicular to the plane vecr*(6hati-3hatj-5hatk)+2=0 . Also, find the point of intersection of this line and the plane.

Find the equation of the line passing through the point with position vector hati-hatj+2hatk and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Find the vector equation of a line passing through a point with position vector 2hati-hatj+hatk and parallel t the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk . Also, find the cartesian equivalent of the equation.

Find the vector equation of the plane passing through three points with position vectors hati+hatj-2hatk, 2hati-hatj+hatk and hati+2hatj+hatk . Also find the co-ordinates of the point of intersection of this plane and the line vecr=3hati-hatj-hatk+lambda(2hati-2hatj+hatk) .

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hati-hatj+4hatk and is in the direction hati + 2hatj - hatk

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (hati+hatj+hatk) = 6 and vecr cdot(2hati + 3hatj+4hatk) = -5 , and the point (1, 1, 1).

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk) =6 and vecr.(2hati+3hatj+4hatk)=-5 and point (1,1,1)