If you are given a line (r=[4,-5,6] + t[2,0,-1], how can you, from that info, figure out 3 planes which intersect at that point?
Hello, theowne!
What point ??If you are given a line: .
how can you, from that info, figure out 3 planes which intersect at that point?
If you're referring to the point
. . write three equations of the form:
. . which have as their solution.
Here's one system: .
I've attached a sketch of three planes with a common line (in red). As you can see you only need a second direction vector (colour of the 2nd vector correspond to the colour of the plane's name) to span a plane.
So choose any numbers for a, b and c to get a new plane which contains the given line:
a = 1, b = 2, c = 3 will yield:
General solution:
The normal vector of the new plane is
Considering that the point A(4, -5, 6) must be in the new plane you'll get the general equation: