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Section 5 Wrap Up Questions

  1. Given a non-zero vector \(\vec{v}\text{,}\) explain how to construct a unit vector that points in the opposite direction to \(\vec{v}\text{.}\)

  2. For two vectors \(\vec{v}\) and \(\vec{w}\text{,}\) the triangle inequality states that \(||\vec{v}+\vec{w}|| \leq ||\vec{v}|| +||\vec{w}||\) is always true.

    1. Give an example of two vectors for which \(||\vec{v}+\vec{w}||\) is strictly less that \(||\vec{v}|| +||\vec{w}||\text{.}\)
    2. Give an example of two vectors for which \(||\vec{v}+\vec{w}||=||\vec{v}|| +||\vec{w}||\text{.}\)
    3. How are \(\vec{v}\) and \(\vec{w}\) be related when \(||\vec{v}+\vec{w}||=||\vec{v}|| +||\vec{w}||\text{?}\)
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