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?

A(1,2,−1), B(2,5,−2) and C(4,4,−3) are three vertices of a rectangle. What is the area of the rectangle?

$ABC$ is a triangle right-angled at B. If A(k,1,−1), B(2k,0,2) and $C(2+2k,k,1)$ are the vertices of the triangle, then what is the value of k?