Hi I'm not sure if this is the right forum, but I apologize if it is not.

I am very new to vectors and am very confused by it, would really appreciate the help!

1.) Determine the nature of triangle ABC using distances: A(0,0,3), B(2,8,1) and C(-9,6,18)

For the lengths, I got AB to be sqrt(24) units

I got BC to be sqrt(414) units

and AC to be sqrt(373) units

So it is not an isoceles or equitorial triangle.

Then I did the dot product

I didn't get zero for all of them..

I had taken AB dot BC, BC dot AC, AC dot AB, wondering if it is right. If it is convenient, can someone explain why you dot like that to me, I do not understand it.

2.) A sphere has a centre C(-1, 2, 4) and diameter [AB] where A is (-2,1,3). Find the coordinates of B and the radius of the circle.

What does [AB] mean! And how do I even do this..

Thank you so much!