### Learning Objectives (Skills)

#### Short term ("This will be on the test.")

1. Find a parametric representation for a plane (defined by an equation or by geometric conditions). (Sec. 1.2)
2. Find the tangent vector (and tangent line) to a parametrized curve at a point, and interpret it in terms of the approximate change of the vector-valued function for a small change of the parameter. (Sec. 1.4)

#### Long term ("Why are we studying this?")

1. Recognize the vector operations of addition, scalar multiplication, and dot product in various contexts: (Sec. 1.1)
• geometrical or physical vectors
• nongeometrical numerical (finite-dimensional) vectors (e.g., business applications)
• functions (infinite-dimensional vectors)
2. Appreciate the difference between points and vectors, and the dependence of the vector operations in physical space upon the choice of origin. (Sec. 1.3)
3. Distinguish the various geometrical representations/interpretations of vector-valued functions. (Sec. 1.4)