## Angle between two vectors

### Task number: 2689

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

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