Activity 9.3.4

In this activity, use Properties of vector operations to simplify each of the following expressions into a single vector of the form $\langle a,b,c \rangle$. For this activity, let $\vu=\langle 1,-2,3 \rangle$, $\vv=\langle 2,-2,5\rangle$, and $\vw=\langle -3,0,3\rangle$.

1. $\vu+2\vv+3\vw$

2. $2\vw-3\vu$

3. $-4(\vv-\vw)$

4. $-2(3\vu)$

5. Give the components of the vector that fills in the blank: $(2\vw-3\vu) - \underline{\hspace{2.5cm}} = \vzero$

6. Explain why the following expression does not make sense: $$\begin{gathered} 2 \langle 2,4,-7 \rangle - 3 \langle -\pi, \sqrt{7} \rangle \end{gathered}$$