[9.4] - Reading Assignment

Read section 9.4 in the textbook.

1. Why is it that if $\myv a \cdot (\myv b \times \myv c)=0$ then $\myv a$, $\myv b$, and $\myv c$ are coplanar?
   

   The vector $\myv n=\myv b \times \myv c$ is certainly perpendicular to $\myv b$ and $\myv c$. If ($\myv a \times \myv b)\cdot \myv c=0$ that means $\myv n$ is perpendicular to $\myv c$ as well. So all three vectors are perpendicular to $\myv n$. And we define a plane as all the vectors which are perpendicular to a particular normal vector $\myv n$. So they're all in the same plane.

2. What is the volume of the parallelepiped defined by the vectors $\myc{1,1,1}$, $\myc{0,1,1}$, and $\myc{1,2,0}$? (Show your calculations)

   
   But the volume should always be a positive number. Instead of worrying about getting the order of the cross products "correct", let's just take any 2 of the vectors as $\myv b$ and $\myv c$, and just take the absolute value of whatever number we get at the end: Volume = 2.

3. What other questions / musings / muddy points from the reading?