"Find the distance from P(3,0,-1) to the plane P described by the equation
4x + 2y - z = 6.
Find the closest point to P which lies on P."
With this question, I basically do not know how you would answer the question to find the distance (given that point and the equation). I had a look at the answer in hope for some direction although, I do not understand why and how you would be able to figure out to find the length of vector P to Q (dot product) n-hat to get the distance. I know that you are able to find the normal vector from the equation although, how are you able to find the point Q that lies on P (this was given in the answer)? Moreover, I'm unsure with how you find the closest point. I would assume that you would need the distance to find it though.
Unfortunately, this was not something that was covered in my lectures nor it is in my textbook so, any help would be appreciated.