Angle between two vectors

Determine the angle between the following pairs of real vectors (if possible, determine the exact value, otherwise the cosine).

Decide whether the angle is acute or obtuse.

Variant 1
\(\mathbf x^T=(1, -4)\), \(\mathbf y^T=(8, 2)\).
Hint
In \(\mathbb R^n\) holds: \(\cos\alpha = \frac{\langle \mathbf x|\mathbf y \rangle}{||\mathbf x||\cdot ||\mathbf y||}\).
Result
\(\cos\alpha=0\), \(\alpha=\frac{\pi}{2}\) (perpendicular vectors, the right angle).
Variant 2
\(\mathbf x^T=(3, 2, -2)\), \(\mathbf y^T=(0, 4, 1)\).
Result
\(\cos\alpha=\frac{6}{17}\), \(\alpha\doteq 69^\circ\) (an acute angle).
Variant 3
\(\mathbf x^T=(0, 0, 1)\), \(\mathbf y^T=(1, 0, -1)\).
Result
\(\cos\alpha=-\frac{\sqrt{2}}{2}\), \(\alpha=\frac{3\pi}{4}\) (an obtuse angle).
Variant 4
\(\mathbf x^T=(3, 4)\), \(\mathbf y^T=(-1, 0)\).
Result
\(\cos\alpha=-\frac{3}{5}\), \(\alpha\doteq 127^\circ\) (an obtuse angle).