Position vectors and distance Quiz

1. $\overrightarrow{OA}=2\mathbf{i}+3\mathbf{j}$ and $\overrightarrow{OB}=5\mathbf{i}-\mathbf{j}$. Find $\overrightarrow{AB}$.

• A. $-3\mathbf{i}+4\mathbf{j}$
• B. $7\mathbf{i}+2\mathbf{j}$
• C. $3\mathbf{i}-4\mathbf{j}$
• D. $3\mathbf{i}+4\mathbf{j}$

2. Find the distance between $(-2,3)$ and $(1,7)$.

• A. $5$
• B. $7$
• C. $\sqrt{7}$
• D. $25$

3. Find the midpoint of $(-4,1)$ and $(6,9)$.

• A. $(2,10)$
• B. $(5,4)$
• C. $(10,8)$
• D. $(1,5)$

4. $\overrightarrow{AB}=3\mathbf{i}-2\mathbf{j}$ and $\overrightarrow{BC}=6\mathbf{i}-4\mathbf{j}$. What can be said about $A$, $B$, $C$?

• A. They form a right-angled triangle
• B. They are collinear
• C. $B$ is the midpoint of $AC$
• D. They form an isosceles triangle

5. $\mathbf{a}=3\mathbf{i}+\mathbf{j}$ and $\mathbf{b}=\mathbf{i}-2\mathbf{j}$ are position vectors of $A$ and $B$. Find $AB$.

• A. $5$
• B. $\sqrt{5}$
• C. $\sqrt{13}$
• D. $13$