Explain why the 3 point A(2,3,-1), B(8,5,-5) and C(-1,2,1) do not determine a plane.

Question

Explain why the 3 point A(2,3,-1), B(8,5,-5) and C(-1,2,1) do not determine a plane.

Explain why the line (x,y,z) = (4,9,-3) + t(1,-4,2), t{any real number} and the point P(8,-7,5) do not determine a plane.

Thank you!

Answer 1

FIRST QUESTION

Because the line determined by the points A, B contains point C

Let us find parametric equations for the line passing through the points A and B.

Vector AB = < 6 , 2, -4 >

The parametric equations for the AB line are

x = 2 + 6t

y = 3 + 2t

z = -1 - 4t

Now notice that for t = -1/ 2 we get the coordinates of point C.

SECOND QUESTION

Because the point belongs to the line. This happens for t = 4