Vectors in two and three dimensions Quiz

1. Find $|2\mathbf{i}+3\mathbf{j}-6\mathbf{k}|$.

• A. $11$
• B. $-1$
• C. $7$
• D. $\sqrt{43}$

2. Find a unit vector in the direction of $2\mathbf{i}-2\mathbf{j}+\mathbf{k}$.

• A. $\frac23\mathbf{i}-\frac23\mathbf{j}+\frac13\mathbf{k}$
• B. $2\mathbf{i}-2\mathbf{j}+\mathbf{k}$
• C. $\frac13(2\mathbf{i}+2\mathbf{j}+\mathbf{k})$
• D. $\frac15(2\mathbf{i}-2\mathbf{j}+\mathbf{k})$

3. $A=(1,2,3)$ and $B=(4,6,3)$. Find $AB$.

• A. $7$
• B. $\sqrt7$
• C. $25$
• D. $5$

4. $A$ has position vector $2\mathbf{i}+\mathbf{j}$ and $B$ has $6\mathbf{i}-3\mathbf{j}$. Find the position vector of the midpoint of $AB$.

• A. $4\mathbf{i}+2\mathbf{j}$
• B. $4\mathbf{i}-\mathbf{j}$
• C. $8\mathbf{i}-2\mathbf{j}$
• D. $-4\mathbf{i}+4\mathbf{j}$

5. The vectors $3\mathbf{i}+p\mathbf{j}+2\mathbf{k}$ and $6\mathbf{i}-4\mathbf{j}+q\mathbf{k}$ are parallel. Find $p+q$.

• A. $2$
• B. $-2$
• C. $4$
• D. $6$