How to find condition of three planes intersecting at a point (according to vector approach)?

Question

For example, if

Plane 1: $2x+y+z=1$

Plane 2: $x-y+z=2$

Plane 3 : $4x-y+3z =5$

How to check if these planes intersecting at a single point? I want to check the coordinates of intersection , from scalar triple product or solving from normals of the planes .

What do you mean by "vector approach"? Writing it in the matrix form $A(x,y,z)^T = b$ involves an unknown vector, so this can be called "vector approach"? — GNUSupporter 8964民主女神地下教會, Sep 30 '18 at 15:21

score 0 · Accepted Answer · answered Sep 30 '18 at 16:19

0

You just have to solve the linear systems formed by the equations of your planes, and to see whether it has solutions or not.

answered Sep 30 '18 at 16:19

TheSilverDoe

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How to find condition of three planes intersecting at a point (according to vector approach)?

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