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

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

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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