Distance from Point to Plane

**Lafexlos** · March 31st 2010, 10:30 AM

Without using distance formula, find the distance from the point (0,0,1) to the plane $\;4y\;+\;3z\;=\;-12\;$

i dont have any idea about how to solve. :S

**elim** · March 31st 2010, 11:40 AM

Originally Posted by Lafexlos

Without using distance formula, find the distance from the point (0,0,1) to the plane $\;4y\;+\;3z\;=\;-12\;$

i dont have any idea about how to solve. :S

$(0,0,-4)$ is clearly on the plane and $(0,4/5,3/5)$ is the unit norm of the plane.

So $|((0,0,1)-(0,0,-4)) \cdot (0,4/5,3/5)| = 3$
is the length of the projection of the segment from $(0,0,-4)$ to $(0,0,1)$ onto the norm of the plane,
thus is the distance between $(0,0,1)$ to the plane.

**Lafexlos** · March 31st 2010, 12:05 PM

Almost i get it but why are you dot producted with normal vector?
Edit: Ok. i get it now. thx for help. =)

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