Find the vector and cartesian equation of a plane which passes through the point `(1,4,6)` and perpendicular to `(hati-2hatj+hatk)`.

Find the vector and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

Find the vector and cartesian equations of the plane which passes through the point (5, 2, 4) and perpendicular to the line with direction ratios (2, 3, 1) .

Find the vector and Cartesian equation of the plane that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

Find the vector and Cartesian equation of the plane that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

Find the vector and the Cartesian equations of the plane passing through the point (1,2,3) and perpendicular to the line with direction ratio 2,3,-4.

Find the vector and Cartesian equation of the plane that passes throgh the point (1,0,-2) and the normal vector to the plane is hati+hatj-hatk.

Find the equation of a line passing through the point (1,2,3) and perpendicular to the plane vecr.(2hati-3hatj+4hatk) = 1 .

Find the vector equationof the line passing through the point (3,1,2) and perpendicular to the plane vecr.(2hati-hatj+hatk)=4 . Find also the point of intersection of this line and the plane.

Find the equation of a line passing through the point (2,-3,5) and parallel to vector (3hati+2hatj-hatk) .

Find the Cartesian equation of the plane passing through point A(1, 2, 3) and which is perpendicular to a vector vecn=2hati-3hatj+4hatk