How do you determine if the vectors are coplanar: a = [-2,-1,4], b = [5,-2,5], and c = [3,0,-1]?
2 Answers
They are coplanar.
Explanation:
Evaluate the determinant of the matrix with these vectors as rows:
#abs((-2, -1, 4),(5,-2,5),(3,0,-1))#
#=-2 abs((-2,5),(0,-1)) -1 abs((5,5),(-1,3))+4 abs((5,-2),(3,0))#
#=-2(2)-1(20)+4(6)#
#=-4-20+24#
#=0#
Since the determinant is
See below
Explanation:
Two non linearly dependent vectors conveniently parametrized, plus a point, generate a plane
with the plane tangent space given by.
Now if
Solving for
so