Find P2 on Plane Given P1 & Dist. 3 Units

[Evien]

If you are given a plane, (x,y,z) = (2,3,0) + s(4,1,5) + t(1,2,6), and you have a point, let's say P1= (2,3,0). How would you find another point on the plane if you know the distance between P1 and the second point is 3 units?

 

[Studiot]

The locus of all points 3 units from a given one is a sphere.

This intersects the given plane in a circle.

So you need additional information to specify the second point you require.

 

[Evien]

Sorry forgot to mention that P1P2 is perpendicular to P1 and P3 (16.25, 0, 0).

 

[Studiot]

So do you not now have two unknowns, s and t, and two known points P1 and P3, that you can use to substitute into find s and t and thence P2?