## 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

$$\mathbf x^T=(1, -4)$$, $$\mathbf y^T=(8, 2)$$.

• #### Variant 2

$$\mathbf x^T=(3, 2, -2)$$, $$\mathbf y^T=(0, 4, 1)$$.

• #### Variant 3

$$\mathbf x^T=(0, 0, 1)$$, $$\mathbf y^T=(1, 0, -1)$$.

• #### Variant 4

$$\mathbf x^T=(3, 4)$$, $$\mathbf y^T=(-1, 0)$$.