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Exam 1 Material: Chapter 12
TIME: 7:00—8:00PM in CAMP 175, 176, and 177
Section 12.2: You should be able to
 Find the vector between two points
 Find the magnitude of a vector
 Represent 2-D and 3-D vectors geometrically
 Be able to add, subtract, and multiply vectors by a scalar and interpret that
actions geometrically
 Express a vector in terms of the basis vectors
 Given a vector, find a unit vector in the same direction
Section 12.2: You should be able to
 Compute the dot product of two vectors (using either definition)
 Use the dot product to determine the angle between two vectors
 Determine if two vectors are orthogonal, parallel, or neither
 Find the scalar and vector projections given two vectors and illustrate the concept
Section 12.4: You should be able to
 Compute the cross product of two 3-D vectors
 Show that the resulting vector from the cross product is orthogonal to the
original two vectors and determine which direction it points
 Determine the angle between two vectors using the cross product or express the
magnitude of the cross product in terms of the angle between the two vectors
 Determine the area of a parallelogram formed by two vectors
 Understand the geometry of a parallelpiped and how to find the volume using the
scalar triple
Section 12.5: You should be able to
 Find the equation of a line in all three forms given sufficient information to
determine a point on the line and the directional vector
 Determine if two lines are parallel, intersecting at one point, or skew
 Determine the equation of a plane given sufficient information to find the normal
vector and a point in the plane
 Determine the point of where a line intersects a plane
 Determine the angle between two planes
 Determine the line of intersection between two planes
Section 12.6: You should be able to
 Sketch cylindrical surfaces
 Identify and (roughly) sketch the quadric surfaces from the Table 1 (page 836) in
this section
Section 12.7: You should be able to
 Convert between rectangular, cylindrical, and spherical coordinates