1. Cancellation law for the cross product
If we have three numbers a ? 0, b and c such that ab = ac, we can cancel the a on
both sides to conclude that b = c. Is this true for cross products, i.e. if $u \neq 0$, and
$u \times v = u \times w$, is it true that $v = w$? Give an argument for why you think it's true
or false.
2. Intersections of lines and plane
In the xy plane, we know that two lines must necessarily intersect at a point if they
are not parallel. Is this true for two lines in 3D? What about two planes in 3D? What
about three planes in 3D? Explain the possibilities.
