Magnitude, direction and position vectors Quiz

1. Find $|-6\mathbf i+8\mathbf j|$.

• A. $2$
• B. $14$
• C. $10$
• D. $\sqrt{28}$

2. Find the direction of $-3\mathbf i+3\mathbf j$, measured anticlockwise from the positive $x$-direction.

• A. $45^\circ$
• B. $135^\circ$
• C. $225^\circ$
• D. $315^\circ$

3. Write the vector of magnitude $10$ and direction $60^\circ$ in component form.

• A. $5\sqrt3\,\mathbf i+5\mathbf j$
• B. $10\mathbf i+60\mathbf j$
• C. $\frac12\mathbf i+\frac{\sqrt3}{2}\mathbf j$
• D. $5\mathbf i+5\sqrt3\,\mathbf j$

4. $A$ and $B$ have position vectors $2\mathbf i-\mathbf j$ and $-\mathbf i+3\mathbf j$. Find the distance $AB$.

• A. $5$
• B. $\sqrt7$
• C. $7$
• D. $\sqrt{13}$

5. Find the unit vector in the direction of $3\mathbf i-4\mathbf j$.

• A. $3\mathbf i-4\mathbf j$
• B. $\frac13\mathbf i-\frac14\mathbf j$
• C. $\frac35\mathbf i-\frac45\mathbf j$
• D. $\frac{3}{7}\mathbf i-\frac47\mathbf j$