Equation of a plane

Question

How do we fins the equation of the line through (-1,3,2) and perpendicular to the plane x+2y+2z=3, the length of the perpendicular and the coordinates of the foot

Answer 1

Try going to a website: mathworld.wolfram.com/Point-PlaneDistance.html

or just google point plane distance, and several websites will come up, with graphical and equations to derive the formula..

Basically you do the dot product of the vector from the point to the plane with the normal vector to the plane. It simplifies (or gets more complex in another sense) to that formula ae+bf+cg+D all over square root of a²+b²+c² The vector from point to plane is (x-e,y-f,z-g) The normal to the plane is (a,b,c)/(a²+b²+c²). Do their dot product and you derive the distance formula where you can plug in the values of the point and the plane.