- Find all of the vectors which satisfy
- Find the shortest length vector which satisfies the relation in part (a).
- We can compute,
So, can take any value, and then we must have for the relation to be satisfied. Therefore, any vector
satisfies the relations.
- So, we know the vectors satisfying the relation are of the form . This means we want to minimize
This is minimal when (since for any other value of ). Then we want to find the value of which minimizes . Taking the derivative and setting it equal to 0 we have
Hence, the vector of minimal length which satisfies the given relation is