1. Show that the two forms of the quadratic formula on page 17 are equivalent (assuming exact…

1. Show that the two forms of the quadratic formula on page 17 are equivalent (assuming exact arithmetic) and explain how to choose one for each root in order to avoid subtracting nearly equal floating point numbers, which leads to loss of precision.

2. Show by counterexample that it is not always true that for 3D vectors a, b, and c, a × (b × c)=(a × b) ×c.

3. Given the non-parallel 3D vectors a and b, compute a right-handed orthonormal basis such that u is parallel to a and v is in the the plane defined by a and b.

 

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