# 1

There are lots-&-lots of equations to the plane.

One equations is gotten by:

> restart : with(linalg):

Warning, new definition for norm

Warning, new definition for trace

> A := [2, 0, 0] ;

> B := [0, 3, 0] ;

> C := [1, 2, 3] ;

> AB := B - A ;

> AC := C - A ;

> N := crossprod( AB, AC);

> f:= simplify( dotprod(N, [x,y,z] - A ) );

So one equation for the plane is:

> f = 0 ;

To check if the three points do indeed satisfy the equation:

> i:= [1,0,0] : j := [0,1,0] : k := [0,0,1]:

> f_eval_at_A := subs( { x=dotprod(A ,i) , y=dotprod(A,j) , z=dotprod(A,k) } , f) ;

> f_eval_at_B := subs( { x=dotprod(B ,i) , y=dotprod(B,j) , z=dotprod(B,k) } , f) ;

> f_eval_at_C := subs( { x=dotprod(C ,i) , y=dotprod(C,j) , z=dotprod(C,k) } , f) ;