• Multivariable Calculus Course Syllabus 

    Unit 3: Vectors and 3-dimensional space

    Goal: The student will demonstrate the ability to use a problem solving approach to apply operations on vectors in two and three dimensions and use vectors to analyze planes, cylinders, and quadric surfaces. Instructor's notes: Students prerequisite knowledge of vectors, parametric equations, matrices and conics should be preassessed before starting this unit. Time will either be saved or added time needed to remediate these topics as student need requires.

    Skills for Unit 3:

    The student will be able to:

    Express vectors in component form and standard basis form.

    Perform basic operations of addition, subtarction and scalar multiplication on vectors, both geometrically and algebraically Compute a unit vector i the direction of a given vector.

    Express a vector as a linear combination of two other vectors.

     Find the length and midpoint of a line segement or vector in three dimensions.

     Calculate dot products and cross products of vectors and interpret geometrically.

    Compute the angle between two vectors.

    Determine whether two vectors are orthogonal.

     Determine and apply the vector projection of one vector along another.

    Interpret and graph points in the 3-dimensional coordinate system.

    Use vectors to define the equations of lines and planes.

    Write the equation of a sphere.

    Determine the equation of a plane in three-dimensional coordinate system and sketch the plane.

    Calculate the distance between a point and a plane.