1. The Right Hand Rule b a
axb

2. Properties of the Cross Product
axb = -bxa
(ca)xb = c(axb) = ax(cb)
ax(b+c) = axb + axc
(a+b)xc = axc + bxc
a.(bxc) = (axb).c
ax(bxc) = (a.c)b-(a.b)c

3. The so-called scalar triple a.(bxc)
But recall that the components of (bxc)
come from 2x2 determinants

4. a.(bxc)
A-ha! We have a quick way to compute this!

5. The Geometric Interpretation Volume of a parallelpiped
V = |bxc| |a||cos( )|=|a.(bxc)|
bxc a h c b
Volume = (Area of Base)*(height)

6. Q. How can we use the cross
product to determine if 3 vectors are
coplanar (lie in the same plane)?
Determine if the volume of the
resulting parallelpiped is nonzero

7. Example Do the following points lie in the same plane? A=(1,-1,2)
B=(2,0,1)
C=(3,2,0)
D=(5,4,2)