# particle with radius 'r' hits the plane. what is the point of contact?

A large particle with radius r hits the plane with perpendicular 'n' and passing through ,q'. I need to check whether it hits the plane or not. In order to do that I need to find the point of contact. My question is: we should shorten the 'p' by r to get the point of contact?

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## 1 Answer

If you represent the particle position by the position of the center of the particle, you can move the plane by one radius along the normal. The particle contacting the plane is the same as the center being in the new plane.

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Without moving the plane how can I find the contact? Can I add the radius r to center of particle p? – nullPointer2 Sep 17 '12 at 15:48
@BadSniper: yes, you can add a length $r$ vector to the point $p$, oriented along the normal to the plane. The result is the same. – Ross Millikan Sep 17 '12 at 15:50
How do I add r? Its a scalar. P is a point. – nullPointer2 Sep 17 '12 at 19:37
@BadSniper: that's why I said a length $r$ vector along the normal to the plane. If $\vec n$ is a unit normal to the plane, you have $p+r\vec n$ – Ross Millikan Sep 17 '12 at 19:52
we have to normalize the orthogonal n and multiply it with r? – nullPointer2 Sep 17 '12 at 19:59