Vectors in problem solving Quiz

1. Parallelogram $ABCD$ has $A(0,0)$, $B(4,1)$, $C(7,5)$. Find $D$.

• A. $(3,4)$
• B. $(11,6)$
• C. $(4,5)$
• D. $(-3,-4)$

2. The forces $(3\mathbf{i}-2\mathbf{j})$ N, $(-\mathbf{i}+5\mathbf{j})$ N and $(x\mathbf{i}+y\mathbf{j})$ N keep a particle in equilibrium. Find $x$ and $y$.

• A. $x=2,\;y=3$
• B. $x=4,\;y=-3$
• C. $x=-2,\;y=3$
• D. $x=-2,\;y=-3$

3. A ship has velocity $(6\mathbf{i}+8\mathbf{j})$ km h$^{-1}$. What is its speed?

• A. $14$ km h$^{-1}$
• B. $10$ km h$^{-1}$
• C. $100$ km h$^{-1}$
• D. $48$ km h$^{-1}$

4. $A$ has position vector $2\mathbf{i}$ and $B$ has $6\mathbf{i}+4\mathbf{j}$. The point $P$ is on $AB$ with $AP:PB=3:1$. Find $\overrightarrow{OP}$.

• A. $4\mathbf{i}+2\mathbf{j}$
• B. $3\mathbf{i}+\mathbf{j}$
• C. $5\mathbf{i}+3\mathbf{j}$
• D. $\frac{10}{3}\mathbf{i}+\frac43\mathbf{j}$

5. $\overrightarrow{AB}=2\mathbf{i}+3\mathbf{j}$ and $\overrightarrow{BC}=4\mathbf{i}+6\mathbf{j}$. Which statement is correct?

• A. $ABC$ is a right-angled triangle
• B. $A$, $B$, $C$ are collinear
• C. $B$ is the midpoint of $AC$
• D. $AB=BC$