SOLUTION: use a determinent to determine whether the given points are coplaner (-4,1,0)(0,1,2)(4,3,-1)(0,0,1)

Question 1043422: use a determinent to determine whether the given points are coplaner
(-4,1,0)(0,1,2)(4,3,-1)(0,0,1)
Found 2 solutions by robertb, Alan3354:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let vector A = <-4,1,0>, B= <0,1,2>, C = <4,3,-1>, and D = <0,0,1>.
We have to find the volume of the parallelipiped formed by the vectors B-A, C-A, and D-A.
The volume is given by the triple vector product [(C-A)x(B-A)]*(D-A).
B-A = <4,0,2>,
C-A = <8,2,-1>, and
D-A = <4,-1,1>.
===> [(C-A)x(B-A)]*(D-A) =
===> the parallelipiped is actually "flat", and the points (-4,1,0), (0,1,2),(4,3,-1), and (0,0,1) are coplanar.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
use a determinent [sic] to determine whether the given points are coplaner [sic]
(-4,1,0)(0,1,2)(4,3,-1)(0,0,1)
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Use the method for determining the volume of a tetrahedron.
If the volume = 0, they're coplanar.
==========
PS it's determinant & coplanar.
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