# Thread: Distance from point to plane

1. ## Distance from point to plane

Find the distance from the point [11, -10, 17] to the plane
-4478 - 283 x + 347 y + 416 z = 0

what i did was i multipled the variables in the plane by their corresponding variables in the point, and then divided that answer by the distance or magnitude of the plane. I got 611.1906 but the computer keep saying that this is not the correct value. Anyone has an alternative solution? Thanks.

2. Originally Posted by purplerain
Find the distance from the point [11, -10, 17] to the plane
-4478 - 283 x + 347 y + 416 z = 0

what i did was i multipled the variables in the plane by their corresponding variables in the point, and then divided that answer by the distance or magnitude of the plane. <<< what exactly is this? I got 611.1906 but the computer keep saying that this is not the correct value. Anyone has an alternative solution? Thanks.
I assume that you calculated:
$\displaystyle d = \dfrac{-4478 - 283 \cdot 11 + 347 \cdot (-10) + 416 \cdot 17}{\sqrt{283^2+347^2+416^2}} = \dfrac{-3989 \cdot \sqrt{41506}}{124516} \approx -6.52661$

The negantive sign of d indicates that the given point and the origin are on different sides of the plane.

3. If the equation of a plane is ax + by + cz + d = 0

Then the distance of a point(x0,y0,z0) to the plane is

D = |ax0 + by0 + cz0 + d|/sqrt(a^2+b^2+c^2)

I get 6.527

4. Oops, yall are right, i recalulated it myself and got approximately 6.480549334. I think the sign should be positive.