# Thread: Finding the normal vector and the distance of point P to the plane

1. ## Finding the normal vector and the distance of point P to the plane

Hi, I'm not sure if I got the right answer to this question, and would really appreciate it if you guys could help me out...

Find the normal vector to the plane through the points Q= (1,1,0), R= (0,0,3) and S= (2,2,1). Hence find the distance from the point P = (1,0,2) to this plane.

I ended up with a normal vector of -4i + 4j and the distance of P to the plane as $\displaystyle \frac{3}{\sqrt{2}}$

Is that correct? Would really appreciate some confirmation on this one.... cheers!

rorosingsong

2. Originally Posted by rorosingsong
Hi, I'm not sure if I got the right answer to this question, and would really appreciate it if you guys could help me out...

Find the normal vector to the plane through the points Q= (1,1,0), R= (0,0,3) and S= (2,2,1). Hence find the distance from the point P = (1,0,2) to this plane.

I ended up with a normal vector of -4i + 4j and the distance of P to the plane as $\displaystyle \frac{3}{\sqrt{2}}$

Is that correct? Would really appreciate some confirmation on this one.... cheers!

rorosingsong
Dear rorosingsong,

Your normal vector is correct. But the distance must be, $\displaystyle \frac{1}{\sqrt{2}}$

3. Ah, thanks! I'm not sure where I went wrong, but I'll go over my working again. Thanks for the prompt reply! =)