**Math 210 Exam 1 Study
Guide**

This is not comprehensive. Some items here may not appear on the exam, and some exam questions may be on material not covered here. However, at a minimum you should know:

- How to compute and the significance of the dot (= 0 for orthogonal vectors) and cross products, including the relation to the cosine and sine of the included angle

- How to find:
- The projection of one vector on another
- The component of one vector along another

- How to find a vector equation of a line given:
- A vector parallel to the line and a point on the line
- Two distinct points on the line

- How to find an equation of a plane given:
- 3 noncollinear points on the plane
- A vector normal to the plane and a point on the plane
- A line in the plane and a point (not on the line) on the plane
- 2 nonparallel vectors parallel to the plane and a point on the plane

- Given
a space curve
**r**, how to find: - The velocity
- Acceleration
- Speed
- Unit tangent vector
- Unit normal vector
- Arc length between two points of the curve

- Differentiation rules for vector valued functions of one real variable:
- Sum
- Scalar multiple
- Product
- Chain