You are watching: Points that lie on the same plane

Take any type of three that the points and determine the equation of the plane. As TonyK said, 3 points always belong to one airplane and, if they execute not every lie in a line, then the identify a unique plane. Once you have the equation the the plane, placed the collaborates of the fourth suggest into the equation to check out if it is satisfied. If the 3 points you made decision

**do**occur to lie on a single line then you room done- any type of fourth point will identify a airplane that all four points lie on.

Hint: analyze by $-A$ so the we have the right to assume $A=(0,0,0)$. Climate points $A,B,C,D$ lied on a aircraft iff vectors $B,C,D$ execute

*not*span whole space, i.e. If $$left| eginarraycccb_1 & b_2 & b_3 \c_1 & c_2 & c_3 \d_1 & d_2 & d_3 endarray ight|=0$$

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