Hello, xfyz!

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.

Let: .

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 volumezero.

Scalar triple product: .

. . .. . . There!