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?

If a line  $\frac{x+1}{p} = \frac{y-1}{q} = \frac{z-2}{r}$  where $p=2q=3r$, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?