The vector product Quiz

1. Find $\mathbf{i}\times\mathbf{j}$.

• A. $-\mathbf{k}$
• B. $\mathbf{k}$
• C. $\mathbf{0}$
• D. $1$

2. If $\mathbf{a}=\mathbf{i}+2\mathbf{j}$ and $\mathbf{b}=3\mathbf{i}+\mathbf{k}$, then $\mathbf{a}\times\mathbf{b}=$

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

3. $|\mathbf{a}\times\mathbf{b}|=12$ and the triangle has sides $\mathbf{a}$ and $\mathbf{b}$. Its area is

• A. $12$
• B. $24$
• C. $4$
• D. $6$

4. The tetrahedron on edges $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$ has $\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})=-18$. Its volume is

• A. $-3$
• B. $18$
• C. $3$
• D. $6$

5. Which statement means $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$ are coplanar?

• A. $\mathbf{a}\times\mathbf{b}=\mathbf{c}$
• B. $\mathbf{a}\cdot\mathbf{b}=0$
• C. $\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})=0$
• D. $|\mathbf{a}\times\mathbf{b}|=1$