Posted by **Jessica** on Thursday, February 24, 2011 at 2:16am.

Use the triple scalar product to determine whether the given points lie in the same plane.

A(1, 2, 3), B(3, -4, 8),

C(7, -1, 1), D(5, 5, -4)

- CALCULUS 3 -
**MathMate**, Thursday, February 24, 2011 at 8:35am
The scalar triple product P among three vectors U,V and W is defined as follows:

P=U.(VxW)

|P| represents the volume of the parallelepiped formed by the vectors U, V and W.

Consequently, if U, V and W are coplanar, P=0.

Since 4 points (A,B,C,D) are given, three vectors can be formed where

U=AB, V=AC, and W=AD.

Calculate the triple scalar product as described above and if the result is zero, then the four points are coplanar.

- CALCULUS 3 -
**Sara**, Monday, September 26, 2011 at 2:02pm
yes

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