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Distance between plane and line

Given the Cartesian or vector equations of a line and a plane, I know that to find whether they are parallel you find the intersection and if this results in an inconsistency (e.g. 0=1) then they are parallel and otherwise they aren't.

If this is the case and they are parallel, how do you use the equations to find the distance between?
Original post by Big-Daddy
Given the Cartesian or vector equations of a line and a plane, I know that to find whether they are parallel you find the intersection and if this results in an inconsistency (e.g. 0=1) then they are parallel and otherwise they aren't.

If this is the case and they are parallel, how do you use the equations to find the distance between?


1. Find the unit normal to the plane n^\bold{\hat{n}}

2. Find a point, P, on the plane by setting, say, x=y=0x=y=0 then finding the corresponding value of zz

3. Find a point, Q, on the line similarly.

4. Find the vector QP\vec{QP}

The distance, d, is then: d=QPn^d = |\vec{QP}\cdot \bold{\hat{n}} |

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