Intersections and distances in three dimensions Quiz

1. The line $\mathbf{r}=(0,1,2)+t(1,1,1)$ meets the plane $x+y+z=6$. At which point?

• A. $(0,1,2)$
• B. $(1,2,3)$
• C. $(2,3,4)$
• D. $(3,4,5)$

2. Find the distance from $(1,2,3)$ to the plane $2x+y+2z-3=0$.

• A. $7$
• B. $\frac79$
• C. $\frac37$
• D. $\frac73$

3. Find the distance from the origin to the plane $3x+4y-12z=26$.

• A. $2$
• B. $26$
• C. $13$
• D. $\frac{2}{13}$

4. The line $\mathbf{r}=(1,1,1)+t(1,2,3)$ and the plane $x+y-z=5$. Which is true?

• A. They meet at exactly one point
• B. The line lies in the plane
• C. The line is parallel to the plane and does not meet it
• D. The line is perpendicular to the plane

5. Find the shortest distance between the lines $\mathbf{r}=s(1,0,0)$ and $\mathbf{r}=(0,0,5)+t(0,1,0)$.

• A. $0$
• B. $5$
• C. $25$
• D. $\sqrt5$