Vectors in two dimensions Quiz

1. Given $\mathbf a=2\mathbf i+3\mathbf j$ and $\mathbf b=-\mathbf i+5\mathbf j$, find $3\mathbf a-2\mathbf b$.

• A. $4\mathbf i+19\mathbf j$
• B. $8\mathbf i-\mathbf j$
• C. $8\mathbf i+19\mathbf j$
• D. $4\mathbf i-\mathbf j$

2. Which vector is parallel to $6\mathbf i-9\mathbf j$?

• A. $-2\mathbf i+3\mathbf j$
• B. $3\mathbf i-2\mathbf j$
• C. $2\mathbf i+3\mathbf j$
• D. $9\mathbf i-6\mathbf j$

3. In triangle $ABC$, $\overrightarrow{AB}=\mathbf p$ and $\overrightarrow{AC}=\mathbf q$. What is $\overrightarrow{BC}$?

• A. $\mathbf p-\mathbf q$
• B. $\mathbf p+\mathbf q$
• C. $\mathbf q-\mathbf p$
• D. $-\mathbf p-\mathbf q$

4. For what value of $k$ is $k\mathbf i+6\mathbf j$ parallel to $2\mathbf i-3\mathbf j$?

• A. $-4$
• B. $4$
• C. $-9$
• D. $9$

5. $M$ is the midpoint of $AB$ and $\overrightarrow{AB}=6\mathbf i-4\mathbf j$. Find $\overrightarrow{AM}$.

• A. $12\mathbf i-8\mathbf j$
• B. $6\mathbf i-4\mathbf j$
• C. $-3\mathbf i+2\mathbf j$
• D. $3\mathbf i-2\mathbf j$