Vectors in two dimensions Quiz

1. Find $|3\mathbf{i}-4\mathbf{j}|$.

• A. $1$
• B. $5$
• C. $7$
• D. $25$

2. Find the unit vector in the direction of $8\mathbf{i}+6\mathbf{j}$.

• A. $\frac{1}{14}(8\mathbf{i}+6\mathbf{j})$
• B. $\frac{1}{100}(8\mathbf{i}+6\mathbf{j})$
• C. $\frac{1}{10}(6\mathbf{i}+8\mathbf{j})$
• D. $\frac{1}{10}(8\mathbf{i}+6\mathbf{j})$

3. Write a vector of magnitude $6$ at $30^\circ$ anticlockwise from the positive $x$-axis in component form.

• A. $3\sqrt{3}\,\mathbf{i}+3\mathbf{j}$
• B. $3\mathbf{i}+3\sqrt{3}\,\mathbf{j}$
• C. $6\mathbf{i}+6\mathbf{j}$
• D. $\frac{\sqrt3}{2}\mathbf{i}+\frac12\mathbf{j}$

4. Which vector is parallel to $2\mathbf{i}-3\mathbf{j}$?

• A. $3\mathbf{i}+2\mathbf{j}$
• B. $2\mathbf{i}+3\mathbf{j}$
• C. $-6\mathbf{i}+9\mathbf{j}$
• D. $6\mathbf{i}-4\mathbf{j}$

5. The vector $-\mathbf{i}-\mathbf{j}$ makes what angle with the positive $x$-axis, measured anticlockwise from $0^\circ$ to $360^\circ$?

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