3.12 Vectors: concepts and algebra Quiz

1. $A(1,4,-2)$ and $B(3,1,0)$. Find $\overrightarrow{AB}$.

• A. $(2,-3,2)$
• B. $(-2,3,-2)$
• C. $(4,5,-2)$
• D. $(2,3,2)$

2. Find $|4\mathbf{i}-4\mathbf{j}+2\mathbf{k}|$.

• A. $2$
• B. $6$
• C. $36$
• D. $10$

3. Which vector is parallel to $\begin{pmatrix}1\\-2\\3\end{pmatrix}$?

• A. $\begin{pmatrix}2\\-4\\3\end{pmatrix}$
• B. $\begin{pmatrix}-1\\2\\3\end{pmatrix}$
• C. $\begin{pmatrix}-3\\6\\-9\end{pmatrix}$
• D. $\begin{pmatrix}3\\-2\\1\end{pmatrix}$

4. $M$ is the midpoint of $AB$, where $\mathbf{a}=(2,0,6)$ and $\mathbf{b}=(4,-2,0)$. Find $\mathbf{m}$.

• A. $(6,-2,6)$
• B. $(1,-1,-3)$
• C. $(3,-1,3)$
• D. $(2,-2,-6)$

5. $\overrightarrow{OX}=2\mathbf{u}$ and $\overrightarrow{OY}=5\mathbf{u}$, $\mathbf{u}\ne\mathbf{0}$. What can you conclude?

• A. $O$, $X$, $Y$ are collinear
• B. $OXY$ is a right-angled triangle
• C. $X$ is the midpoint of $OY$
• D. $|\overrightarrow{XY}|=7|\mathbf{u}|$