Let $Q=(0,0,0)$ be a point in $\mathbb{R}^3$...

Question

Let $Q=(0,0,0)$ be a point in $\mathbb{R}^3$.

$P1$ and $P2$ are two planes in $\mathbb{R}^3$

$P1: x-y+2z=1$

$P2: 2x + y + z=4$

A) Find the general form of the equation of the Plane $P3$ through $Q$ that is parallel to $P1$.

B) Find the point-normal form of the equation of the plane $P4$ through $Q$ and perpendicular to the line of the intersection of $P1$ and $P2$

My input:

I have no idea where to begin from this, if someone could give me a pointer.

I've tried searching google for similar questions but I haven't had much luck as either the questions are more harder than this one.

I just need a hint in the right direction for both of these questions.

Any help will be greatly appreciated.

Answer 1

You need to remember the following facts about planes and lines.

The normal vector to the plane $$ ax+by+cz=d$$ is the vector $$<a,b,c>$$

Two planes are parallel if the normal vectors are parallel.

Finding the line of intersection of two planes is as easy as finding two points on the intersection of the planes.