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Section 6 Wrap Up Questions

  1. Answer the following as True or False with a brief reason.

    1. If \(\vec{v} \times \vec{w} =\vec{0}\text{,}\) then \(\vec{v}\) and \(\vec{w}\) are perpendicular.
    2. If \(\vec{v}\) and \(\vec{w}\) are non-zero vectors in 3-space and \(\vec{v} \cdot \vec{w}=0\text{,}\) then \(\vec{v} \times \vec{w} \neq \vec{0}\text{.}\)
    3. You can use the dot product to find a normal vector to a plane given any three points in that plane.
    4. For any three vectors \(\vec{v}\text{,}\) \(\vec{w}\text{,}\) and \(\vec{u}\text{,}\) we have \((\vec{u} \times \vec{v} )+\vec{w}=(\vec{u} +\vec{w}) \times (\vec{v} +\vec{w})\text{.}\)
  2. The cross product and dot product are both ways to multiply two vectors. Describe some of the differences between these two multiplications.
  3. Why does the cross-product not make sense in 2-space?
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