What figure do these 3D vectors make?

[superams]

Homework Statement

The vertices of a figure are given by A(-8, 4, -2), B(-6, 3, 5), and C(-10, 5, -9). What type of figure is ABC? Why?

Homework Equations

pythagorean theorem: |AB|=√(x^2+y^2+z^2)

The Attempt at a Solution

I first found the vector AB, BC, and CA by subtracting the components of the vectors.
Then I calculation the magnitude of |AB|, |BC|, and |CA| using the pythagorean theorem.
I got this |AB|=3√6 |BC|=6√6 and |CA|=3√6
According to my calculation, point A is on the line connecting points B and C, so the 3 points are collinear and form a line.

But the answer seems wrong since they are asking for a type of a figure.

 

[voko]

The vectors are indeed linearly interdependent, your conclusion is correct.