Activity 9.7.3

Let $P_0 = (1,2,-1)$, $P_1 = (1, 0 ,-1)$, and $P_2 = (0,1,3)$ and let $p$ be the plane containing $P_0$, $P_1$, and $P_2$.

1. Determine the components of the vectors $\overrightarrow{P_0P_1}$ and $\overrightarrow{P_0P_2}$.

2. Find a normal vector $\vn$ to $p$.

3. Find a scalar equation of $p$.

4. Consider a second plane $q$ with scalar equation $-3(x-1) + 4(y+3) + 2(z-5)=0$. Find two different points on $q$ as well as a vector $\vm$ that is normal to $q$.

5. What is the angle between planes $p$ and $q$?