1. Find a vector parallel to the vector and a vector orthogonal to it.
2. Find the angle between the vectors
3. What is the length of the 10-dimensional vector Find a vector orthogonal to u and normalize each vector.
4. Verify the Cauchy-Schwarz and triangle inequalities for the vectors
5. Explain the result of applying the Cauchy-Schwarz inequality to the vectors
6. Prove the parallelogram law Explain where its name
comes from by considering vectors
in the plane.
7. Determine if all possible pairings of the following vectors are parallel, orthogonal or neither
8. Show that the triangle formed by the points (−3, 5, 6), (−2, 7, 9), and (2, 1, 7) is a 30-60-90 triangle