the points are a(1,1,1), b(-4,1,6) c(1,0,4) d(-2,2,2)
2007-08-02 07:19:52 · 2 answers · asked by moooona1987 2 in Science & Mathematics ➔ Mathematics
They are not. If they were colinear, a and b wouldn't be able to have the same y-coordinate unless all four points had the same y-coordinate, which they don't.
2007-08-02 07:23:32 · answer #1 · answered by DavidK93 7 · 2⤊ 0⤋
There is a general solution to this.
Similar to your coplanar question, construct vectors from a single point, say point a. Then the cross product of any pair of vectors must be zero.
Specifically:
(b - a) x (c - a) = ( 5, 15, 5) so a,b,c are not colinear
(b - a) x (d - a) = (-5, -10, -5) so a, b, d are not colinear
(c - a) x (d - a) = (-4, -9, -3) so a, c, d are not colinear
(c - b) x (d - b) = (6, 16, 7) so b, c, d are not colinear
Not only are all 4 not colinear, no set of 3 is colinear either.
2007-08-04 14:04:26 · answer #2 · answered by Pretzels 5 · 0⤊ 0⤋