Show that the points (-1,4,-3) , (3,2,-5) , (-3,8,-5) and (-3,2,1) are coplanar?
2 Answers
They are not coplanar . Still i could always be wrong !
Explanation:
using the four points , we can create 3 vectors with one of the point as common origin.
A(-1,4,-3) ; B(3,2,-5); C(-3,8,-5); D(-3,2,1)
i take A as common origin (doesn't matter which one you take) .
So i create 3 vectors AB , AC , and AD.
Take take the cross product of any of the two vectors(this will give you a resulting vector which is normal to the plane ) and perform the dot product of the result with the remaining vector .
If you get 0 as the result , then the four points are coplanar
I'm taking cross product of AB and AC
now dot product this result with AD
= 8
Therefore they are not coplanar .
I can always be wrong !
lie in a single plane
Explanation:
Let
Since two rows in the determinant are same
determinant vanishes to zero.
Thus,
lie in a single plane