Vectors in three dimensions Quiz

1. Find $|2\mathbf i-2\mathbf j+\mathbf k|$.

• A. $1$
• B. $5$
• C. $9$
• D. $3$

2. Find the distance between $(1,2,3)$ and $(3,-2,5)$.

• A. $2\sqrt6$
• B. $\sqrt{12}$
• C. $24$
• D. $2\sqrt3$

3. Which vector is parallel to $2\mathbf i-4\mathbf j+6\mathbf k$?

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

4. A particle starts at $\mathbf i+\mathbf j+\mathbf k$ with constant velocity $2\mathbf i-\mathbf j+3\mathbf k$. Where is it after $2$ s?

• A. $3\mathbf i+0\mathbf j+4\mathbf k$
• B. $5\mathbf i-\mathbf j+7\mathbf k$
• C. $4\mathbf i-2\mathbf j+6\mathbf k$
• D. $5\mathbf i+3\mathbf j+7\mathbf k$

5. The paths of two moving bodies cross at a point. Does this mean they collide?

• A. Yes: crossing paths always means a collision.
• B. Yes, if their speeds are equal.
• C. No: they must also be at that point at the same time.
• D. No: bodies in three dimensions can never collide.