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Reflections 12.7 Reflect on your understanding
In addition to the reflection activities below, re-read
Section 12.2 Terminology and notation . Be sure you understand each of the new definitions introduced in this chapter, and spend some time committing them to memory.
1. Vector norm in \(\R^2 \) .
2. Unit vectors and normalization.
State the definition of
unit vector and explain how to create a unit vector parallel to a given vector.
3. Distance.
Explain how a vector norm can be used to determine the distance between two points or between two vectors.
4. Dot product as algebra-geometry bridge.
State the connection between the dot product, vector norm, and angle between vectors.
5. Norm as dot product.
State how a vector norm can be computed using the dot product.
6. Dot product as matrix product.
State how the dot product can be computed as a matrix product of column vectors.
