You made some errors in the first one.
I'll correct them.
1) Determine the nature of triangle ABC with vertices: A(0,0,3), B(2,8,1) and C(-9,6,18)
For the lengths, I got AB to be sqrt(72) units
I got BC to be sqrt(414) units
and AC to be sqrt(342) units
So it is not an isoceles or equilateral triangle. . Right!
Given two vectors and if
We have: .
Therefore, is a right triangle.
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 sphere.
Did you make a sketch?
Going from A to C, we move:Code:A r C r B * - - - - - * - - - - - * (-2,1,3) (-1,2,4) (x,y,z)
. . +1 in the x-direction, +1 in the y-direction, and +1 in the z-direction.
Going from C to B, we make the same moves: