I'm still working on #1 . . . don't know why it's giving me trouble.
2. Find the cross product for: .
I set up the matrix: .
and came out with: .
We have: .
It took me a minute to remember what the scalar triple product is for.3. Use the scalar triple product to determine whether the points:
lie on the same plane.
Given three vectors , the scalar triple product, gives us
the volume of the parallelepiped ("slanted box") determined by the vectors.
The three vectors have a common point,
If the vectors point in three "different" directions (like the legs of a tripod),
. . the parallelepiped will have a volume (greater than zero).
If the vectors are in the same plane, then the "box" will have volume zero.
Scalar triple product: .
. . . . . . There!