Orthogonality relation

Task number: 2691

W.r.t. the standard scalar product decide which pairs of the following three vectors are orthogonal: \((1, 2, 3)\), \((5, 2, -3)\) and \((-2, -1, -4)\).

Which of the following properties has the relation of orthogonality: reflexivity, irreflexivity, symmetry, antisymmetry, transitivity?

  • Resolution

    \((1, 2, 3)\perp(5, 2, -3)\), \((5, 2, -3)\perp(-2, -1, -4)\), but \((1, 2, 3)\not\perp(-2, -1, -4)\).

    Hence the orthogonality is not transitive (nor reflexive, only symmetric).

Difficulty level: Easy task (using definitions and simple reasoning)
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