Vectors

  • vector geometry
  • AIMS Maxwell 2021

    Let \begin{align} \boldsymbol{\vec a} &= \boldsymbol{\hat x}-3\boldsymbol{\hat y}-\boldsymbol{\hat z}\\ \boldsymbol{\vec b} &= \boldsymbol{\hat x}+\boldsymbol{\hat y}+2\boldsymbol{\hat z}\\ {\boldsymbol{\vec c}} &= -2\boldsymbol{\hat x}-\boldsymbol{\hat y}+\boldsymbol{\hat z}\\ \boldsymbol{\vec d} &= -\boldsymbol{\hat x}-\boldsymbol{\hat y}+\boldsymbol{\hat z} \end{align}

    Use the dot product to determine which pairs (if any) of these vectors

    1. Are perpendicular?
    2. Are parallel?
    3. Have an angle less than \(\pi/2\) between them?
    4. Have an angle of more than \(\pi/2\) between them?