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:


  1. 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


  1. How to find:
    1. The projection of one vector on another
    2. The component of one vector along another


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


  1. How to find an equation of a plane given:
    1. 3 noncollinear points on the plane
    2. A vector normal to the plane and a point on the plane
    3. A line in the plane and a point (not on the line) on the plane
    4. 2 nonparallel vectors parallel to the plane and a point on the plane


  1. Given a space curve r, how to find:
    1. The velocity
    2. Acceleration
    3. Speed
    4. Unit tangent vector
    5. Unit normal vector
    6. Arc length between two points of the curve


  1. Differentiation rules for vector valued functions of one real variable:
    1. Sum
    2. Scalar multiple
    3. Product
    4. Chain