Vector and cartesian equation of line

The foot of the perpendicular drawn from the origin O to a plane is N(12,-4,-3). Find the equation of the plane in cartesian form and vector form.

Equation of plane in normal form

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hat i-hat j+4hat k and is in the direction hat i+2hat j-hat k

Equation of normal in Point form

Angle between two lines in vector and cartesian form

Find the equation of plane in Cartesian form which is at a distance of 5 unit from origin and its normal vector from origin is parallel to a vector formed by joining points A(1, 2, 3) and B(3, -4, -6).

Find the equation of plane in Cartesian form which is at a distance 3/sqrt(41) from origin and its normal vector from origin is 3hati-4hatj-4hatk

The foot of the perpendicular drawn from the origin to a plane is (4,-2,-5) . Find the equation of the plane in (i) vector form, ii) Cartesian form.

Find the vector equations of the plane whose cartesian form of equation is 5x - 7x + 2z = 3.