[9.4] - Reading Assignment
Read section 9.4 in the textbook.
- 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.
- What is the volume of the parallelepiped defined by the vectors
$\myc{1,1,1}$, $\myc{0,1,1}$, and $\myc{1,2,0}$?
Answer: 2. So show your calculations...
- What other questions / musings / muddy points from the reading?