Consider the vectors shown in the figure.

Part 1: Basic properties

The figure shows vectors in [math] for [math] . The coordinate representation of the zero vector is [math] (use coordinate vector notation, not ijk-vector notation).

Part 2: Parallel or not?

Are any two of these vectors parallel to each other?
  • Is [math] parallel to [math]?
  • Is [math] parallel to [math]?
  • Is [math] parallel to [math]?

Part 3: Coordinate representations

Find the coordinate representations of each vector:
  • [math]
  • [math]
  • [math]

Part 4: Finding relationships among these vectors

Write each of the vectors in terms of the other vectors. Use the names of vectors in your answer (e.g., enter 4a2 - 5a3 for [math]). Do not enter coordinate representations such as [math].
  • [math]
  • [math]
  • [math]

Part 5: Can we combine these vectors to get the zero vector?

If possible, scale and add the vectors [math], [math], and [math] to obtain the zero vector [math]. If this is not possible, enter DNE.
Use the names of vectors in your answer (e.g., enter 4a1 - 5a2 + a3 for [math]). Do not enter coordinate representations such as [math].
[math]