The figure shows vectors in $\mathbb{R}^n$ for $n =$ . The coordinate representation of the zero vector is $\vec{0} =$ (use coordinate vector notation, not ijk-vector notation).

Are any two of these vectors parallel to each other?

• Is $\vec{a}_1$ parallel to $\vec{a}_2$? choose parallel not parallel cannot be determined
• Is $\vec{a}_1$ parallel to $\vec{a}_3$? choose parallel not parallel cannot be determined
• Is $\vec{a}_2$ parallel to $\vec{a}_3$? choose parallel not parallel cannot be determined

Find the coordinate representations of each vector:

• $\vec{a}_1 =$
• $\vec{a}_2 =$
• $\vec{a}_3 =$

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 $4 \vec{a}_2 - 5 \vec{a}_3$). Do not enter coordinate representations such as $\langle 3, 4 \rangle$.

• $\vec{a}_1 =$
• $\vec{a}_2 =$
• $\vec{a}_3 =$

If possible, scale and add the vectors $\vec{a}_1$, $\vec{a}_2$, and $\vec{a}_3$ to obtain the zero vector $\vec{0}$. If this is not possible, enter DNE.
Use the names of vectors in your answer (e.g., enter 4a1 - 5a2 + a3 for $4 \vec{a}_1 - 5 \vec{a}_2 + \vec{a}_3$). Do not enter coordinate representations such as $\langle 3, 4 \rangle$.
$= \vec{0}.$