For the following two (02) items:
Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) B(0, 1, 0) and C(0, 0, 1)

On which one of the following planes does the centre of S lie?

For the following two (02) items:
Let A(1, - 1, 0) B(- 2, 1, 8) and C(- 1, 2, 7) are three consecutive vertices of a parallelogram ABCD.

What is the fourth vertex D?

For the following two (02) items:
Let A(1, - 1, 0) B(- 2, 1, 8) and C(- 1, 2, 7) are three consecutive vertices of a parallelogram ABCD.

If angle BCD is $\theta $ then what is $ cos^2 \theta$ equal to?

If a line in 3 dimensions makes angles α, β and γ with the positive directions of the coordinate axes, then what is $\cos (\alpha +\beta )\cos (\alpha -\beta )$ equal to?