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# Download Exam 1 Material: Chapter 12

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Transcript

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 geometrically 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