The scalar product Quiz

1. Find $(3\mathbf{i}+\mathbf{j}-2\mathbf{k})\cdot(\mathbf{i}-4\mathbf{j}+\mathbf{k})$.

• A. $9$
• B. $3$
• C. $-9$
• D. $-3$

2. Find the value of $k$ for which $2\mathbf{i}+k\mathbf{j}+3\mathbf{k}$ is perpendicular to $\mathbf{i}-\mathbf{j}+\mathbf{k}$.

• A. $k=-5$
• B. $k=5$
• C. $k=1$
• D. $k=-1$

3. Vectors $\mathbf{a}$ and $\mathbf{b}$ have $\mathbf{a}\cdot\mathbf{b}=-6$, $|\mathbf{a}|=3$ and $|\mathbf{b}|=4$. Find the angle between them.

• A. $60^\circ$
• B. $120^\circ$
• C. $150^\circ$
• D. $30^\circ$

4. Two non-zero vectors have $\mathbf{a}\cdot\mathbf{b}>0$. What does this tell you?

• A. The vectors are perpendicular
• B. The vectors are parallel
• C. The angle between them is acute
• D. The angle between them is obtuse

5. Find $|\mathbf{a}|$ if $\mathbf{a}=\mathbf{i}-2\mathbf{j}+2\mathbf{k}$.

• A. $3$
• B. $5$
• C. $\sqrt{5}$
• D. $1$