In the end, most times, you can add an additive constant "+C". It is not done here.
Length of \([1,-2,2]\)? We have \(|[1,-2,2]|=\sqrt{1^2+(-2)^2+2^2}=\sqrt{9}=3\)
Dot product of \([1,-2,2]\) and \([4,5,6]\)? It's \(1\cdot 4-2\cdot 5+2\cdot 6=6\)
Angle between [3,4] and [-3,4]? Unit vectors are [0.6,0.8] and [-0.6,0.8]. Their dot product is 0.64-0.36=0.48. We have \(\alpha=\acos(0.48)\approx 61.31^\circle\).
Cross product of \([1,-2,2]\) and \([4,5,6]\)? By OctaveOnline it is \([-22,2,13]\)