Lines and planes (Scalar equation + pt. of int.)

[Lornt]

so I've been doing review and I got stuck on two questions, I was wondering if anyone could help me out.
Any help would be appericiated - whether it's a hint on what my first step should be or what's the final answer to confirm whether I'm right or wrong :)


1. Find the scalar equation of the plane that passes through the point (1, 1, 4) and is perpendicular to the line of intersection of the planes x + 2y + z = 1 and 2x + y + 3z = 3.


2. Determine the distance from the point P(2, 3, -1) to the plane 2x + y - 2z + 9 = 0. (I know I can plug the values into the equation, but that doesn't really help me. Could anyone show me a longer way to do this involving more steps? I don't really understand where the equation comes from).

 

[Hurkyl]

1. Find the scalar equation of the plane that passes through the point (1, 1, 4) and is perpendicular to the line of intersection of the planes x + 2y + z = 1 and 2x + y + 3z = 3.

Start simple, and build up a solution.

What is the scalar equation equation for a plane?
How do you tell if a plane passes through a point?
What is the scalar equation for a plane passing through that point?
What is the line of intersection of those two planes?
How do you tell if a plane is perpendicular to a line?
What is the scalar equation for a plane perpendicular to that line?
What is the scalar equation for a plane passing through that point and perpendicular to that line?

This is a basic problem solving technique: it's useful in just about anything you do.

2. Determine the distance from the point P(2, 3, -1) to the plane 2x + y - 2z + 9 = 0. (I know I can plug the values into the equation, but that doesn't really help me. Could anyone show me a longer way to do this involving more steps? I don't really understand where the equation comes from).

Starting with definitions is another basic problem solving technique.

What is the definition of the distance from a point to a plane?

 

[HallsofIvy]

so I've been doing review and I got stuck on two questions, I was wondering if anyone could help me out.
Any help would be appericiated - whether it's a hint on what my first step should be or what's the final answer to confirm whether I'm right or wrong :)


1. Find the scalar equation of the plane that passes through the point (1, 1, 4) and is perpendicular to the line of intersection of the planes x + 2y + z = 1 and 2x + y + 3z = 3.


2. Determine the distance from the point P(2, 3, -1) to the plane 2x + y - 2z + 9 = 0. (I know I can plug the values into the equation, but that doesn't really help me. Could anyone show me a longer way to do this involving more steps? I don't really understand where the equation comes from).

We could better "confirm whether I'm right or wrong" if you would show us what you have done.

 

[Kidphysics]

http://www.jtaylor1142001.net/calcjat/Solutions/VPlanes/VPPtLine.htm

little late but help for anyone who types this question into a search engine