1. Verify that a line re?ection in 3-D can be performed as a rotation. Which rotation? Give the axis and angle. Verify that this re?ection can be applied to any blade.

2. Show that the fact that the geometric product transforms naturally under applica- tion of a versor, together with linearity, implies that the contraction is preserved. (Hint: An intermediate step uses linearity to show that the outer product is preserved.)

3. Compute the meet and join of two parallel vectors u and v. The meet should now be symmetric. (Hint: Use one of them as the join.)